Education.com
Try
Brainzy
Try
Plus

# Magnetism Study Guide (page 3)

(not rated)
By
Updated on Sep 27, 2011

## Magnetic Field Created by an Electric Current

As we learned in the previous section, an electric current is acted upon by a magnetic force. Our question now is: Does an electric current influence or create a magnetic field? The answer to this can be demonstrated with a battery, a wire, and a compass. In the presence of current through the wire, the compass is deflected from its normal position showing the magnetic field of Earth.

If we consider a long, current -carrying wire, the compass around the wire will show magnetic field lines of a circular pattern with direction influenced by the direction of the current through the wire. Again, the right-hand rule can be used to determine the magnetic field direction this time.

Experimentally, one can find the value of the magnetic field, its dependence on the current strength, and the distance relative to the wire.

In Figure 15.8, we show the magnetic field vector drawn as a vector tangent to the magnetic field line, and the size of the vector decreases with increased distance from the wire.

The magnetic field generated by a long, straight wire transporting an electrical current I at a point around the wire is proportional to the value of the current and inversely proportional to the relative distance to the wire.

The constant μ0 is called permeability of the vacuum, and its universal value is:

μ0 = 4 · π · 10– 7 T · m/ A

Magnetic field around the wire decreases as the larger the distance as shown in the equation. The pictorial interpretation in Figure 15.9 shows magnetic field lines at different distances from the current (concentric circles).

r2r1 < r3r2 < r4r3

In the presence of a current passing through a wire, a charge moving in proximity will be affected by the magnetic field produced by the wire, in the same manner as it would be affected by the same field created by a magnet.

### Determining Direction of the Magnetic Field

To determine the direction, the extended thumb of the right hand points in the direction of the current, and the fingers are wrapped around the wire. The fingers will point in the direction of the magnetic field.

#### Example 1

Consider a positive charge moving in an upward direction and in close proximity to a magnetic field, such as the one in Figure 15.10. Find the direction of the magnetic force on the charge.

#### Solution 1

As seen in the figure, the current I is creating a magnetic field. The magnetic field line shows the direction of the field according to the application of the righthand rule. The vector describes a counterclockwise direction.

The magnetic force is seen to be oriented perpendicular to the plane of the velocity and the magnetic field and (for this case) toward the center of the circle. This means that the linear trajectory of the particle is going to be affected and curved as a result of the magnetic interaction.

If the wire in the previous figure affects a moving charge, then it could affect a number of charges, thus forming a current. So, the logical conclusion is that two currents in proximity to each other will affect each other. Because both currents determine a magnetic field around them, their interaction can be of attraction or of repulsion depending on the field, hence of the current.

#### Example 2

Find the type of interaction between two parallel wires in which electrical currents flow in the same direction.

#### Solution 2

Start by drawing the parallel wires and their corresponding flow (see Figure 15.11). Then figure the direction of the magnetic field, and, based on what we learned about the interaction between magnets, figure the type of interaction in this example.

The significance of the diagram is that the two wires behave as two magnets with opposite poles close to each other, and, as you may remember, this means that the two wires will attract each other.

There will also be a magnetic force acting on each of these wires because the magnetic field created by a current will interact with the electric current passing through the second wire as shown in Figure 15.12.

The general expression we learned in the previous sections was:

F = I · L · B · sin α

The angle between the current and the magnetic field is 90°; therefore, the sin of 90° = 1.

F = I · L · B

The force on wire 1 then is:

F1 = I1 · L · B2

Whereas the force on the second wire, considering the same length, is:

F2 = I2 · L · B1

If we also consider the expression of the magnetic field:

For each of the currents, the magnetic field is:

The distance between the two wires is the same. Then the forces become:

And on the second current:

The two expressions are identical, which means that each current will influence the other current with the same strength.

Practice problems of this concept can be found at: Magnetism Practice Questions

150 Characters allowed

### Related Questions

#### Q:

See More Questions

### Today on Education.com

#### HOLIDAYS

The 2013 Gift Guide Is Here

#### HOLIDAYS

Hands-On Hanukkah: 8 Crafts to Do Now
Top Worksheet Slideshows