Allan.J.Wilson: April 2020

Thursday 30 April 2020

Corona updates 30-4-2020 India

MAHARASHTRA: 583 new cases; tally rises to 10,498
GUJARAT: 313 new cases today; total climbs to 4,395
DELHI: 76 new cases; total climbs to 3,515
MADHYA PRADESH: 65 new cases; total climbs to 2,625
RAJASTHAN: 146 more test positive; total climbs to 2,584
TAMIL NADU: 161 new cases; tally climbs to 2,323
UTTAR PRADESH: 77 fresh cases; total climbs to 2,211
TELANGANA: 22 new cases; total climbs to 1,038
WEST BENGAL: 36 new cases; tally rises to 794
JAMMU & KASHMIR: 33 new cases; tally at 614
KARNATAKA: 30 new cases; total climbs to 565
KERALA: 2 new cases; tally at 497
PUNJAB: 105 cases today; tally rises to 480
BIHAR: 13 new cases today; total climbs to 422
HARYANA: 28 fresh cases; tally at 339
ODISHA: 14 new cases reported; total climbs to 142
JHARKHAND: 3 new cases; total rises to 110
CHANDIGARH: 7 new cases; total climbs to 74
UTTARAKHAND: 2 new cases today; tally rises to 57
ASSAM: 5 more test positive; total climbs to 42
CHHATTISGARH: 2 more test positive; tally at 40
HIMACHAL PRADESH: Tally remains at 40

Tuesday 28 April 2020

Corona updates 28-4-2020

MAHARASHTRA: 729 new cases; tally rises to 9,318
GUJARAT: 226 new cases, ttally rises to 3,774
DELHI: 206 fresh cases; tally climbs to 3,314
MADHYA PRADESH: 58 new cases; tally rises to 2,387
RAJASTHAN: 102 positive cases, tally rises to 2,364
TAMIL NADU: 121 new cases; tally now at 2,058
UTTAR PRADESH: 66 more cases; tally rises to 2,053
TELANGANA: 6 new positive cases; tally rises to 1,009
WEST BENGAL: 28 new cases; tally rises to 663
JAMMU & KASHMIR: 19 new cases reported; tally rises to 565
KARNATAKA: 11 cases confirmed; tally at 523
KERALA: Four more COVID-19 cases in Kerala;tally now 485
BIHAR: 20 more test positive; total reaches 366
PUNJAB: 12 new cases; tally rises to 342
ODISHA: 7 new cases; total rises to 118
JHARKHAND: 2 more COVID-19 cases, tally rises to 105
UTTARAKHAND: 3 more test positive; tally rises to 54
ASSAM: 2 test positive; tally rises to 37
LADAKH: 2 more test positive; number of cases now at 22

Monday 27 April 2020

Corona updates 27-4-2020 India

MAHARASHTRA: 522 new positive cases & 27 deaths today; tally rises to 8,590
GUJARAT: 247 new cases; tally rises to 3,548
DELHI: 190 fresh cases; tally climbs to 3,108
RAJASTHAN: 77 more cases reported today; tally rises to 2,262
UTTAR PRADESH: 113 more test positive; total confirmed cases at 1,986
TAMIL NADU: 52 new cases; taking total number of cases to 1,937
ANDHRA PRADESH: 80 new cases; tally rises to 1,177
TELANGANA: Two moretest positive; tally rises to 1,003
JAMMU & KASHMIR: Death toll at 7; tally at 546
KARNATAKA: 9 new cases, total cases at 512
KERALA: 13 new COVID-19 positive cases; tally now 481
BIHAR: 19 more persons test positive, taking the tally to 345
PUNJAB: 8 new cases today; tally rises to 330
HARYANA: 5 new cases; tally rises to 301
ODISHA: 7 fresh COVID-19 cases reported, total mounts to 110
JHARKHAND: 7 new cases reported today; total number of cases rise to 98
UTTARAKHAND: No new COVID19 case reported today; tally stands at 51
CHANDIGARH: 5 new cases reported; tally rises to 45
HIMACHAL PRADESH: No new case; total count stays at 41

Corona updates 27-4-2020 India

PM Modi reportedly told nine Chief Ministers that the lockdown had saved thousands of lives in the past one and a half months.
"We have to give importance to the economy as well as continue the fight against COVID-19," PM Modi told Chief Ministers.
Economic activities are likely to reopen in orange and green districts, which have far fewer cases or none.
States, said the PM, must make efforts to covert red zones into orange and then into green zones.
Private cars may be allowed with restrictions but the ban on public transport, including trains, flights and buses, is likely to continue.
Schools and colleges are likely to stay shut and the ban on religious meetings and congregations will also continue.
Five of nine Chief Ministers at the meeting said the lockdown should end, while the rest were in favour of extending it for the sake of controlling the spread of COVID-19.
Among those who favoured continuing the lockdown were Odisha, Meghalaya and Goa. Odisha asked for a month's extension of the restrictions.
"Green zones will be opened, relaxations in sectors have been agreed to but the mindset of lockdown will continue. We should get people ready with new norms like social distancing," said Meghalaya Chief Minister Conrad Sangma after the meeting.
Kerala Chief Minister Pinarayi Vijayan skipped the meeting and sent the Chief Secretary to represent the state.

Sunday 26 April 2020

Corona updates 26-4-2020 India

Tamil Nadu CM has announced a complete lockdown in Chennai from April 26-29, between 6 AM & 9PM.
29 new cases recorded in Jammu and Kashmir, total crosses 500-mark.
India reported close to 2,000 new cases in 24 hours, count nears 27,000.
India and Mexico are its worst-impacted international operations due to the Covid-19, says Hershey's.
IITs, IIITs not to hike tuition fee for 2020 academic session.
Saudi Arabia extends suspension of flights, public transport till further notice.
Madhya Pradesh becomes the third state with over 100 deaths..
Telangana became the ninth state to breach the 1,000-mark, active patients at 660.
9 CMs likely to speak at tomorrow's video-conference with PM Modi.
Recovery rate of patients climbs to 21.97%; Kerala has best recovery rate at 74%.
The first Covid-19 patient to be administered convalescent plasma therapy in India was discharged from the hospital.

Friday 24 April 2020

Corona updates 23-4-2020 India

Wrap Up: All you need to know about Covid-19 pandemic

MAHARASHTRA: 18 deaths & 394 new cases; death toll at 310; case tally at 6,817
GUJARAT: 15 deaths & 191 new cases; tally at 2,815
DELHI: 138 new cases & 3 deaths today; total death toll at 53; cases rise to 2,514
RAJASTHAN: 70 new cases; tally at 2,034
MADHYA PRADESH: 7 deaths; 75 more cases; tally at 1,846
TAMIL NADU: 2 deaths; 72 more cases; tally rises to 1,755
TELANGANA: 13 new COVID19 cases, total rises to 983
KARNATAKA: 29 new cases; total number at 474
JAMMU & KASHMIR: 27 new cases; tally rises to 454
KERALA: Death of a 4-month-old; 3 more test positive; tally at 450
WEST BENGAL: 51 more cases; tally rises to 385
PUNJAB: 70 cured & 17 deaths from a tally of 298
HARYANA: 5 fresh cases; total count 275
BIHAR: 21 more test positive; tally at 197
ODISHA: 5 more test positive; total count at 94
JHARKHAND: 2 new cases; tally at 59
UTTARAKHAND: 1 new case; tally to 48
HIMACHAL PRADESH: 1 death & 18 recovered from a tally of 40
CHANDIGARH: No new cases today; tally stands at 27

Monday 20 April 2020

Corona updates 21-4-2020 India

Around 100 people working at the Rashtrapati Bhavan complex have been quarantined after a sanitation worker tested positive for coronavirus, sources have said.
The doubling rate of coronavirus cases - considered a marker of how fast the infection is spreading - has slowed down, the government said on Monday. Based on the last seven days, India's doubling rate has improved to 7.5 days from 3.4 days before the lockdown, senior health ministry official Lav Agarwal told the media. On that basis, the government earlier said the three-week nationwide lockdown proved effective and extended it till May 3.
Delhi reported the country's first plasma therapy success story on Monday. A 49-year-old man who got treatment at a private hospital in the city has recovered. The patient is now off ventilator support, the Saket branch of Max Hospital said.
Maharashtra, the state with the highest number of coronavirus patients, will allow the use of anti-malaria drug hydroxychloroquine in parts of the state, including Dharavi - Asia's largest slum- as a precautionary measure against the disease, the state government has said.
Across India, restrictions were eased on Monday in the non-containment zones to boost economic activity in line with announcements made by Prime Minister Narendra Modi last week. The central government, however, has told states and union territories that the guidelines on the countrywide shutdown cannot be diluted.
India's top medical body - the Indian Council of Medical Research - has said it would replace all the defective COVID-19 testing kits in West Bengal after the state raised the issue. The state government had said that faulty kits supplied by ICMR were throwing up inconclusive results and delaying the pace of testing.
Telangana is the first state to extend the lockdown till May 7. Chief Minister K Chandrashekar Rao has said the lockdown will be enforced in a stringent manner, and the food delivery mobile applications will not be allowed. "The cabinet will take stock of the situation on May 5," he said.
After Uttar Pradesh, five more states will make arrangements to bring back their students stranded in coaching hub Kota in Rajasthan because of the nationwide coronavirus lockdown, Chief Minister Ashok Gehlot said on Monday. Madhya Pradesh, Bengal, Gujarat, Chhattisgarh and Assam are ready to take their students back from Kota, Mr Gehlot said.
Worldwide, more than 24 lakh people have coronavirus, nearly 170,000 have died. US has reported the highest number of COVID-19 cases with 230,000 cases, more than 42,000 deaths have been reported from the country.
The 193 members of the UN General Assembly on Monday adopted by consensus a resolution that calls for "equitable, efficient and timely" access to any future vaccines developed to fight coronavirus. The resolution also highlights the "crucial leading role" played by the World Health Organization, which has faced criticism from Washington and others about its handling of the pandemic.

Corona updates 20-4-2020 India

India has seen an improvement in the recovery rate that indicates the number of people who have successfully fought off the illness, according to Union Health Ministry. The rate stood at 14.75 per cent this morning, an improvement over 14.19 per cent on Sunday, 13.85 per cent on Saturday, 13.06 per cent on Friday, Thursday's 12.02 per cent, Wednesday's 11.41 per cent and Tuesday's 9.99 per cent. More than 2,500 patients across the country have recovered from the highly infectious illness so far.
Prime Minister Narendra Modi on Sunday said the COVID-19 pandemic affects everyone equally. "COVID-19 does not see race, religion, colour, caste, creed, language or border before striking. Our response and conduct thereafter should attach primacy to unity and brotherhood. We are in this together," PM Modi said in a post on LinkedIn.
"Coronavirus has significantly changed the contours of professional life. These days, home is the new office. The Internet is the new meeting room. For the time being, office breaks with colleagues are history... I have also been adapting to these changes. Most meetings, be it with minister colleagues, officials and world leaders, are now via video conferencing," said the Prime Minister, who has been holding video conferences with chief ministers and other leaders to review the lockdown and the road ahead.
In Telangana, Chief Minister K Chandrashekar Rao has announced extension of the coronavirus lockdown till May 7. He said the lockdown will be enforced in a stringent manner, and the food delivery mobile applications will not be allowed starting Monday. "The cabinet has decided to extend the lockdown in the state till May 7. The cabinet will take stock of the situation on May 5," he said.
All airlines have been told by the aviation regulator - Directorate General of Civil Aviation or DGCA - to not take bookings after May 3 when the second phase of lockdown is scheduled to end. Air traffic and passenger trains were suspended last month, days before the nationwide shutdown began on March 25.
West Bengal government has said that faulty kits supplied by the Indian Council for Medical Research (ICMR), the country's nodal body for COVID-19 testing, have been throwing up inconclusive results and delaying the pace of testing. While an ICMR response is awaited, the director of the Council's nodal body in Kolkata said that the matter was being seriously addressed.
More relaxations are likely if India tackles coronavirus crisis well, Union Minister Prakash Javadekar told news agency PTI on Sunday.
There are 54 districts in 14 states that have not reported any fresh cases during the last 14 days, Union Health Ministry official Lav Agarwal said on Sunday during a press briefing, news agency PTI reported.
More than 4,000 cases reported across India have been linked to the congregation held in south Delhi's Nizammudin last month by the Islamic sect Tablighi Jamaat, the government said on Saturday. "A total of 4,291 COVID-19 cases or 29.8 per cent of the 14,378 coronavirus infections reported till Saturday morning are linked to the Tablighi Jamaat congregation," Union Health Ministry's Lav Agarwal had said on Saturday.
India may touch its peak of coronavirus cases in the first week of May, after which the number will decline, sources in the Home Ministry have said.

Saturday 18 April 2020

Corona updates 19-4-2020

The recovery rate that indicates the number of people who have successfully fought off the illness is improving, Union Health Ministry has said. The rate stood at 14.19 per cent this morning, an improvement over 13.85 per cent on Saturday, 13.06 per cent on Friday, Thursday's 12.02 per cent, Wednesday's 11.41 per cent and Tuesday's 9.99 per cent. So far, 2,231 patients in India have recovered from the highly infectious illness.
There are 22 new districts in 12 states that have not reported any fresh cases during the last 14 days, Union Health Ministry official Lav Agarwal said on Saturday during a press briefing, news agency PTI reported.
More than 4,000 cases reported across India have been linked to the congregation held in south Delhi's Nizammudin last month by the Islamic sect Tablighi Jamaat, the government said on Saturday. "A total of 4,291 COVID-19 cases or 29.8 per cent of the 14,378 coronavirus infections reported till Saturday morning are linked to the Tablighi Jamaat congregation," Union Health Ministry's Lav Agarwal told reporters.
With over 3,600 COVID-19 cases, Maharashtra continues to remain the worst hit state in the country. The number of cases in Mumbai's Dharavi, Asia's largest slum rose to 117 on Saturday.
In Delhi, one of the worst affected cities in the country, Chief Minister Arvind Kejriwal on Saturday warned people of the dangers of not following social distancing advice during the lockdown by citing the case of a neighbourhood in the national capital, where 26 people were found infected with COVID-19. "In Jahangirpuri, 26 people of the same family tested positive. They lived next to each other and despite containment measures, they continued visiting each other. We are worried for you," Mr Kejriwal said in a video briefing.
In Uttar Pradesh's Gautam Buddha Nagar district, one of the worst affected in the state by the outbreak, the top medical officer has been replaced for the second time in a month. The twin cities of Noida-Greater Noida are a part of this district.
Two districts in Jammu and Kashmir where over 300 coronavirus cases have been reported including five deaths have flattened the curve, officials have said. There is no active COVID case in Rajouri and Kishtwar districts after four COVID positive patients recovered and no new case has been reported in the last 10 days.
Amid the fight against COVID-19, attacks continue on health workers and those providing essential services. In the latest incident, a group of sanitation worker in Madhya Pradesh were attacked by a mob of locals in Dewas district on Friday when they went to a neighbourhood to clean the streets. In Bihar, four such cases of attack on health workers were reported across the state within 24 hours on Thursday. PM Modi has repeatedly urged people across the country to support those providing essential services in doing their jobs
India may touch its peak of coronavirus cases in the first week of May, after which the number will decline, sources in the Home Ministry have said.
Worldwide, over 1.5 lakh people have died due to coronavirus, which originated in China's Wuhan city in December; more than 20 lakh are infected. The global economy, already "sluggish" before the coronavirus outbreak, is now bound to suffer a "severe recession" in 2020, IMF chief Kristalina Georgieva has warned and said the current crisis posed "daunting challenges" for policymakers in many emerging markets and developing economies.

Friday 17 April 2020

Corona updates 18-4-2020 India

Indian Navy has reported its first set of COVID-19 cases. Twenty-one sailors in Mumbai have tested positive. A massive operation to trace people who may have come in contact with them is on. The sailors were staying in the residential accommodation facilities of INS Angre - a shore-based depot that provides logistical and administrative support to naval operations of the Western Naval Command.
In Mumbai's Dharavi - Asia's largest slum - the number of coronavirus cases has crossed the 100-mark. Fifteen new cases were reported on Friday, which takes the total to 101. The city, with 2,073 coronavirus cases, is the worst affected city in the country; Maharashtra is the worst hit state. The city of 1.2 crore has been under a complete lockdown since the last month.
The recovery rate that indicates the number of people who have successfully fought off the illness is improving, Union Health Ministry has said. The rate stood at 13.85 per cent this morning, an improvement over 13.06 per cent on Friday, Thursday's 12.02 per cent, Wednesday's 11.41 per cent and Tuesday's 9.99 per cent. On Friday, 260 patients were declared cured from COVID-19 and discharged from hospitals. On Thursday, 183 were discharged from hospitals after they recovered.
Indian scientists are testing a multi-purpose vaccine that has proven to be effective against leprosy and boosts immunity in hosts to see if it can help tackle the coronavirus, the chief of country's largest public-funded research institution told NDTV on Friday. "With the approval of the DCGI (Drug Controller General of India), we have begun tests on the MW vaccine that has been successfully used against leprosy," Dr Shekhar Mande, Director General of the Council of Scientific and Industrial Research (CSIR), said.
Kerala is making the case for a 28-day isolation period after a man in Kannur, who returned from Dubai and showed no symptoms of coronavirus, tested positive nearly a month later. At present, a 14-day quarantine period is the norm.
Amid a countrywide lockdown, health officials and policemen are being targeted. In Bihar, four such cases of attack on health workers were reported across the state within 24 hours on Thursday. Two of them took place in Bihar Sharif, the hometown of Chief Minister Nitish Kumar. On Wednesday, a team of doctors and other medical staff were attacked in in neighbouring Uttar Pradesh's Moradabad, when they went to take primary contacts of a COVID 19 patient who died, to a quarantine facility. PM Modi has repeatedly urged people across the country to support those providing essential services in doing their jobs.
India may touch its peak of coronavirus cases in the first week of May, after which the number will decline, sources in the Home Ministry have said.
After continuing a strict lockdown till April 20, the districts that are not virus hotspots will be allowed to resume some industrial, construction and manufacturing activities as the government attempts to restart the economy and move towards a gradual exit from the nationwide shutdown to prevent the infection from spreading rapidly.
Rajasthan, Punjab and Bihar, which were the first few states to announce lockdowns, have managed to avoid sharp jumps in positive cases compared to states that went for partial curbs at first like Uttar Pradesh, Gujarat and Maharashtra.
The World Health Organization said on Friday that many countries would likely follow China in revising up their death counts once they start getting the coronavirus ~~crisis~~ under control. Wuhan, where COVID-19 originated in December, on Friday admitted missteps in tallying its death count, abruptly raising the city's count by 50 percent -- following growing world doubts about Chinese transparency over the outbreak.

Corona updates 17-4-2020 India

An internal government assessment suggests that India may touch its peak of coronavirus cases in the first week of May, after which the number will decline, sources in the Home Ministry have said.
"The next one week is crucial. India is going to ramp up its testing. All those who have symptoms related to Severe Acute Respiratory Infection will be tested," a senior bureaucrat told NDTV.
The government has made new additions to the list of activities that will be allowed amid lockdown in parts of the country that are least affected by coronavirus. Non-banking finance corporations and micro-finance institutions will be marked essential services that can resume. Coconut, spice bamboo, areca nut and cocoa plantations, and forest produce by scheduled tribes have also been added to the list.
Construction in rural areas of water supply and sanitation and laying of power lines and telecom optical fibres and cables will also be allowed, according to a notification put out by the Home Ministry.
After continuing a strict lockdown till April 20, the districts that are not virus hotspots will be allowed to resume some industrial, construction and manufacturing activities as the government attempts to restart the economy and move towards a gradual exit from the nationwide shutdown to prevent the infection from spreading rapidly.
Rajasthan, Punjab and Bihar, which were the first few states to announce lockdowns, have managed to avoid sharp jumps in positive cases compared to states that went for partial curbs at first like Uttar Pradesh, Gujarat and Maharashtra.
Rajasthan has 1,131 infected patients and 164 recoveries. According to data collected by the Home Ministry, the state has 7,448 people in isolation as of Thursday.
Though Delhi added 424 cases between Tuesday and Wednesday, the number of people in quarantine came down 15,327 to 14,504. Officials who are crunching the numbers say that states like Andhra Pradesh and Madhya Pradesh are the big cause of worry.
Attacks on health officials have peaked in Bihar, with four cases being reported across the state within 24 hours. Two of them took place in Bihar Sharif, the hometown of Chief Minister Nitish Kumar.
On Wednesday, a team of doctors and other medical staff were attacked in Moradabad, located in neighbouring Uttar Pradesh, when they went to take primary contacts of a COVID 19 patient who died, to a quarantine facility.

Wednesday 15 April 2020

Corona updates 16-4-2020 India

A "hotspot (red zone) classification" would be districts or cities contributing to more than 80 per cent of the cases in the country or the state. Places that show a high rate of infection -- doubling rate less than four days - will also be in this category.
For a concerted push against the virus in red zones, the government said there should be special teams to conduct door-to-door surveys and tests. The tests will not just be for COVID-19. Patients of influenza-related illness and SARI (severe acute respiratory illness), will also be tested, since such patients have often tested positive for coronavirus.
Some industries in rural areas, e-commerce, IT and farming will be allowed after April 20, the government said on Wednesday in new guidelines a day after Prime Minister Narendra Modi extended the nationwide coronavirus lockdown till May 3 and said restrictions would be relaxed after a week in the least infected parts of India.
The government says it will also allow the construction of roads and buildings in rural areas and the manufacture of IT hardware to reduce the distress of millions during a prolonged lockdown to slow the spread of coronavirus.
States will be responsible for ensuring that all safety and social distancing protocols are in place, the home ministry guidelines say. The exemptions won't apply to hotspots. PM Modi extended the restrictions as India crossed 10,000 coronavirus cases despite a 21-day lockdown.
The inter-state transport of goods, essential and non-essential items, will be allowed after April 20. Highway dhabas, truck repair shops and call centres for government activities can reopen from April 20. So can manufacturing units of pharmaceuticals and medical equipment.
Manufacturing and other industrial establishments with access control will be allowed in special economic zones, industrial estates and industrial townships after implementation of SOP (standard operating procedure) for social distancing. Manufacture of IT hardware and of essential goods and packaging can resume.
All air, train and road travel, educational institutions; non-essential industrial and commercial activities, hotels, cinema halls, shopping complexes, theatres stay closed. Social, political and other events, religious centres and gatherings will also not be allowed.
The country's top medical Indian Council of Medical Research (ICMR) on Wednesday said that a research study in China has shown that the coronavirus strain at the heart of the global COVID-19 pandemic is a mutated form of its variant found in bats.
"As per a research in China, it was found that coronavirus might have mutated in bats so as to infect humans," said ICMR's head scientist Dr Raman R Gangakhedkar. "There is also a possibility that bats might have transmitted it to pangolins, and from pangolins it got transmitted to humans," he said.

EC 8451 Electromagnetic Fields Unit- 5 Plane Electromagnetic Waves

Electromagnetic waves

In the previous chapter we introduced the equations pertaining to wave propagation and discussed how the wave equations are modified for time harmonic case. In this chapter we discuss in detail a particular form of electromagnetic wave propagation called 'plane waves'.

The Helmhotz Equation:

In source free linear isotropic medium, Maxwell equations in phasor form are,

is called the wave number or propagation constant of the medium.

Plane waves in Lossless medium:

In Cartesian coordinates each of the equations 6.1(a) and 6.1(b) are equivalent to three scalar Helmholtz's equations, one each in the components Ex, Ey and Ez or Hx , Hy, Hz.

For example if we consider Ex component we can write

A uniform plane wave is a particular solution of Maxwell's equation assuming electric field (and magnetic field) has same magnitude and phase in infinite planes perpendicular to the direction of propagation. It may be noted that in the strict sense a uniform plane wave doesn't exist in practice as creation of such waves are possible with sources of infinite extent. However, at large distances from the source, the wavefront or the surface of the constant phase becomes almost spherical and a small portion of this large sphere can be considered to plane. The characteristics of plane waves are simple and useful for studying many practical scenarios.

Let us consider a plane wave which has only Ex component and propagating along z . Since the plane wave will have no variation along the plane

are the amplitude constants (can be determined from boundary conditions).

As can be seen from the figure, at successive times, the wave travels in the +z direction.

Where 'C' is the speed of light. That is plane EM wave travels in free space with the speed of light.

The wavelength l is defined as the distance between two successive maxima (or minima or any other reference points).

Which represents the magnetic field of the wave traveling in the +z direction.

For the negative traveling wave,

For the plane waves described, both the E & H fields are perpendicular to the direction of propagation, and these waves are called TEM (transverse electromagnetic) waves.

The E & H field components of a TEM wave is shown in Fig 6.2.

TEM Waves:

So far we have considered a plane electromagnetic wave propagating in the z-direction. Let us now consider the propagation of a uniform plane wave in any arbitrary direction that doesn't necessarily coincides with an axis.

For a uniform plane wave propagating in z-direction

z =constant denotes a plane of constant phase and uniform amplitude.

If the region under consideration is charge free,

Plane waves in a lossy medium :

In a lossy medium, the EM wave looses power as it propagates. Such a medium is conducting with conductivity σ and we can write:

We have already discussed how an external electric field can polarize a dielectric and give rise to bound charges. When the external electric field is time varying, the polarization vector will vary with the same frequency as that of the applied field. As the frequency of the applied filed increases, the inertia of the charge particles tend to prevent the particle displacement keeping pace with the applied field changes. This results in frictional damping mechanism causing power loss.

In addition, if the material has an appreciable amount of free charges, there will be ohmic losses. It is customary to include the effect of damping and

Let us now consider a plane wave that has only x -component of electric field and propagate along z .

Poynting Vector and Power Flow in Electromagnetic Fields:

Electromagnetic waves can transport energy from one point to another point. The electric and magnetic field intensities asscociated with a travelling electromagnetic wave can be related to the rate of such energy transfer.

Let us consider Maxwell's Curl Equations:

the above curl equations we can write

Applying Divergence theorem we can write,

the power dissipation within the volume. Hence right hand side of the equation (6.36) represents the total decrease in power within the volume under consideration.

The left hand side of equation (6.36) can be written as

is called the Poynting vector and it represents the power density vector associated with the electromagnetic field. The integration of the Poynting vector over any closed surface gives the net power flowing out of the surface. Equation (6.36) is referred to as Poynting theorem and it states that the net power flowing out of a given volume is equal to the time rate of decrease in the energy stored within the volume minus the conduction losses.

Poynting vector for the time harmonic case:

Polarisation of plane wave:

The polarisation of a plane wave can be defined as the orientation of the electric field vector as a function of time at a fixed point in space. For an electromagnetic wave, the specification of the orientation of the electric field is sufficent as the magnetic field components are related to electric field vector by the Maxwell's equations.

Let us consider a plane wave travelling in the +z direction. The wave has both Ex and Ey components.

Depending upon the values of Eox and Eoy we can have several possibilities:

1. If Eoy = 0, then the wave is linearly polarised in the x-direction.

2. If Eoy = 0, then the wave is linearly polarised in the y-direction.

3.If Eox and Eoy are both real (or complex with equal phase), once again we get a linearly polarised wave with the axis of polarisation inclined at an

Figure 6.5 : Plot of E(o,t)

From equation (6.47) and figure (6.5) we observe that the tip of the arrow representing electric field vector traces qn ellipse and the field is said to be elliptically polarised.

The polarisation ellipse shown in figure 6.6 is defined by its axial ratio(M/N, the ratio of semimajor to semiminor axis), tilt angle ψ (orientation with respect to xaxis) and sense of rotation(i.e., CW or CCW).

Linear polarisation can be treated as a special case of elliptical polarisation, for which the axial ratio is infinite.

In our example, if |Eox| = |Eoy|, from equation (6.47), the tip of the arrow representing electric field vector traces out a circle. Such a case is referred to as Circular Polarisation. For circular polarisation the axial ratio is unity.

Figure 6.7: Circular Polarisation (RHCP)

Further, the circular polarisation is aside to be right handed circular polarisation (RHCP) if the electric field vector rotates in the direction of the fingers of the right hand when the thumb points in the direction of propagation-(same and CCW). If the electric field vector rotates in the opposite direction, the polarisation is asid to be left hand circular polarisation (LHCP) (same as CW).

In radio communication, different information signals can be transmitted at the same frequency at orthogonal polarisation ( one signal as vertically polarised other horizontally polarised or one as RHCP while the other as LHCP) to increase capacity. Otherwise, same signal can be transmitted at orthogonal polarisation to obtain diversity gain to improve reliability of transmission.

Behaviour of Plane waves at the inteface of two media:

We have considered the propagation of uniform plane waves in an unbounded homogeneous medium. In practice, the wave will propagate in bounded regions where several values of e,μ,σ will be present. When plane wave travelling in one medium meets a different medium, it is partly reflected and partly transmitted. In this section, we consider wave reflection and transmission at planar boundary between two media.

Because of the presence of the second medium at z =0, the incident wave will undergo partial reflection and partial transmission.

Applying boundary conditions at the interface z = 0, i.e., continuity of tangential field components and noting that incident, reflected and transmitted field components are tangential at the boundary, we can write

is called the reflection coefficient.

From equation (6.52), we can write

Let us now consider specific cases:

Case I: Normal incidence on a plane conducting boundary

From (6.53) and (6.54)

t = -1

and T =0

Hence the wave is not transmitted to medium 2, it gets reflected entirely from the interface to the medium 1.

Proceeding in the same manner for the magnetic field in region 1, we can show that,

Case2: Normal incidence on a plane dielectric boundary

If the medium 2 is not a perfect conductor (i.e.

) partial reflection will result. There will be a reflected wave in the medium 1 and a transmitted wave in the medium 2.Because of the reflected wave, standing wave is formed in medium 1.

From equation (6.49(a)) and equation (6.53) we can writ

From (6.61), we can see that, in medium 1 we have a traveling wave component with amplitude TEio and a standing wave component with amplitude 2JEio.

The location of the maximum and the minimum of the electric and magnetic field components in the medium 1from the interface can be found as follows.

The electric field in medium 1 can be written as

Oblique Incidence of EM wave at an interface

So far we have discuss the case of normal incidence where electromagnetic wave traveling in a lossless medium impinges normally at the interface of a second medium. In this section we shall consider the case of oblique incidence. As before, we consider two cases

i. When the second medium is a perfect conductor.

ii. When the second medium is a perfect dielectric.

A plane incidence is defined as the plane containing the vector indicating the direction of propagation of the incident wave and normal to the interface. We study two specific cases when the incident electric field

is parallel to the plane of incidence (parallel polarization). For a general case, the incident wave may have arbitrary polarization but the same can be expressed as a linear combination of these two individual cases.

Oblique Incidence at a plane conducting boundary

i. Perpendicular Polarization

The situation is depicted in figure 6.10.

Since the incident wave is considered to be perpendicular to the plane of incidence, which for the present case happens to be xz plane, the electric field has only y-component.

Therefore,

Similarly, we can write the reflected waves as

From eqns (6.76) and (6.77) we observe that

The wave propagating along the x direction has its amplitude varying with z and hence constitutes a non uniform plane wave. Further, only electric field (Bar E1) is perpendicular to the direction of propagation (i.e. x), the magnetic field has component along the direction of propagation. Such waves are called transverse electric or TE waves.

ii. Parallel Polarization:

Figure 6.11: Parallel Polarization

With reference to fig (6.11), the field components can be written as:

Incident field components:

Since the total tangential electric field component at the interface is zero.

E1 (x,0) + E((x,0) = 0

Substituting these quantities in (6.79) and adding the incident and reflected electric and magnetic field components the total electric and magnetic fields can be written as

propagating wave, magnetic field is in transverse direction, such waves are called transverse magnetic or TM waves.

Oblique incidence at a plane dielectric interface

We continue our discussion on the behavior of plane waves at an interface; this time we consider a plane dielectric interface. As earlier, we consider the two specific cases, namely parallel and perpendicular polarization.