Magnetic field associated with a current

Magnetic field associated with a current (ESBPS)

If you hold a compass near a wire through which current is flowing, the needle on the compass will be deflected.

Since compasses work by pointing along magnetic field lines, this means that there must be a magnetic field near the wire through which the current is flowing.

The magnetic field produced by an electric current is always oriented perpendicular to the direction of the current flow. Below is a sketch of what the magnetic field around a wire looks like when the wire has a current flowing in it. We use B→" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">B⃗ $\overrightarrow{B}$ to denote a magnetic field and arrows on field lines to show the direction of the magnetic field. Note that if there is no current there will be no magnetic field.

The direction of the current in the conductor (wire) is shown by the central arrow. The circles are field lines and they also have a direction indicated by the arrows on the lines. Similar to the situation with electric field lines, the greater the number of lines (or the closer they are together) in an area the stronger the magnetic field.

Important: all of our discussion regarding field directions assumes that we are dealing with conventional current.

To help you visualise this situation, stand a pen or pencil straight up on a desk. The circles are centred around the pencil or pen and would be drawn parallel to the surface of the desk. The tip of the pen or pencil would point in the direction of the current flow.

You can look at the pencil or pen from above and the pencil or pen will be a dot in the centre of the circles. The direction of the magnetic field lines is counter-clockwise for this situation.

To make it easier to see what is happening we are only going to draw one set of circular fields lines but note that this is just for the illustration.

If you put a piece of paper behind the pencil and look at it from the side, then you would be seeing the circular field lines side on and it is hard to know that they are circular. They go through the paper. Remember that field lines have a direction, so when you are looking at the piece of paper from the side it means that the circles go into the paper on one side of the pencil and come out of the paper on the other side.

When we are drawing directions of magnetic fields and currents, we use the symbols ⊙" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">⊙$\odot$ and ⊗" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">⊗$\otimes$. The symbol ⊙" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">⊙$\odot$ represents an arrow that is coming out of the page and the symbol ⊗" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">⊗$\otimes$ represents an arrow that is going into the page.

It is easy to remember the meanings of the symbols if you think of an arrow with a sharp tip at the head and a tail with feathers in the shape of a cross.

The Danish physicist, Hans Christian Oersted, was lecturing one day in 1820 on the possibility of electricity and magnetism being related to one another, and in the process demonstrated it conclusively with an experiment in front of his whole class. By passing an electric current through a metal wire suspended above a magnetic compass, Oersted was able to produce a definite motion of the compass needle in response to the current. What began as a guess at the start of the class session was confirmed as fact at the end. Needless to say, Oersted had to revise his lecture notes for future classes. His discovery paved the way for a whole new branch of science - electromagnetism.

We will now look at three examples of current carrying wires. For each example we will determine the magnetic field and draw the magnetic field lines around the conductor.

Magnetic field around a straight wire (ESBPT)

The direction of the magnetic field around the current carrying conductor is shown in Figure 10.1.

Figure 10.1: Magnetic field around a conductor when you look at the conductor from one end. (a) Current flows out of the page and the magnetic field is counter-clockwise. (b) Current flows into the page and the magnetic field is clockwise.

Figure 10.2: Magnetic fields around a conductor looking down on the conductor. (a) Current flows clockwise. (b) current flows counter-clockwise.

Direction of a magnetic field

Using the directions given in Figure 10.1 and Figure 10.2 try to find a rule that easily tells you the direction of the magnetic field.

Hint: Use your fingers. Hold the wire in your hands and try to find a link between the direction of your thumb and the direction in which your fingers curl.

There is a simple method of finding the relationship between the direction of the current flowing in a conductor and the direction of the magnetic field around the same conductor. The method is called the Right Hand Rule. Simply stated, the Right Hand Rule says that the magnetic field lines produced by a current-carrying wire will be oriented in the same direction as the curled fingers of a person's right hand (in the “hitchhiking” position), with the thumb pointing in the direction of the current flow.

Your right hand and left hand are unique in the sense that you cannot rotate one of them to be in the same position as the other. This means that the right hand part of the rule is essential. You will always get the wrong answer if you use the wrong hand.

The Right Hand Rule

Use the Right Hand Rule to draw in the directions of the magnetic fields for the following conductors with the currents flowing in the directions shown by the arrows. The first problem has been completed for you.

1.		2.		3.		4.
5.		6.		7.		8.
9.		10.		11.		12.

Magnetic field around a current carrying conductor

Apparatus

1.  

   one 9" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">9$\text{9}$ V" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">V$\text{V}$ battery with holder

2.  

   two hookup wires with alligator clips

3.  

   compass

4.  

   stop watch

Method

1. Connect your wires to the battery leaving one end of each wire unconnected so that the circuit is not closed.

2. Be sure to limit the current flow to 10" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">10$\text{10}$ seconds" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">seconds$\text{seconds}$ at a time (Why you might ask, the wire has very little resistance on its own so the battery will go flat very quickly). This is to preserve battery life as well as to prevent overheating of the wires and battery contacts.

3.  

   Place the compass close to the wire.

4. Close the circuit and observe what happens to the compass.

5. Reverse the polarity of the battery and close the circuit. Observe what happens to the compass.

Conclusions

Use your observations to answer the following questions:

1. Does a current flowing in a wire generate a magnetic field?

2. Is the magnetic field present when the current is not flowing?

3. Does the direction of the magnetic field produced by a current in a wire depend on the direction of the current flow?

4. How does the direction of the current affect the magnetic field?

Magnetic field around a current carrying loop (ESBPV)

So far we have only looked at straight wires carrying a current and the magnetic fields around them. We are going to study the magnetic field set up by circular loops of wire carrying a current because the field has very useful properties, for example you will see that we can set up a uniform magnetic field.

Magnetic field around a loop of conductor

Imagine two loops made from wire which carry currents (in opposite directions) and are parallel to the page of your book. By using the Right Hand Rule, draw what you think the magnetic field would look like at different points around each of the two loops. Loop 1 has the current flowing in a counter-clockwise direction, while loop 2 has the current flowing in a clockwise direction.

If you make a loop of current carrying conductor, then the direction of the magnetic field is obtained by applying the Right Hand Rule to different points in the loop.

Notice that there is a variation on the Right Hand Rule. If you make the fingers of your right hand follow the direction of the current in the loop, your thumb will point in the direction where the field lines emerge. This is similar to the north pole (where the field lines emerge from a bar magnet) and shows you which side of the loop would attract a bar magnet's north pole.

Magnetic field around a solenoid (ESBPW)

If we now add another loop with the current in the same direction, then the magnetic field around each loop can be added together to create a stronger magnetic field. A coil of many such loops is called a solenoid. A solenoid is a cylindrical coil of wire acting as a magnet when an electric current flows through the wire. The magnetic field pattern around a solenoid is similar to the magnetic field pattern around the bar magnet that you studied in Grade 10, which had a definite north and south pole as shown in Figure 10.3.

Figure 10.3: Magnetic field around a solenoid.

Real-world applications (ESBPX)

Electromagnets

An electromagnet is a piece of wire intended to generate a magnetic field with the passage of electric current through it. Though all current-carrying conductors produce magnetic fields, an electromagnet is usually constructed in such a way as to maximise the strength of the magnetic field it produces for a special purpose. Electromagnets are commonly used in research, industry, medical, and consumer products. An example of a commonly used electromagnet is in security doors, e.g. on shop doors which open automatically.

As an electrically-controllable magnet, electromagnets form part of a wide variety of “electromechanical” devices: machines that produce a mechanical force or motion through electrical power. Perhaps the most obvious example of such a machine is the electric motor which will be described in detail in Grade 12. Other examples of the use of electromagnets are electric bells, relays, loudspeakers and scrapyard cranes.