Chapter 24, Problem 83A

a.

To determine

Whether the magnetic fields by two parallel wires carrying current in the opposite direction be larger or smaller than individual fields of the wires.

Explanation of Solution

Introduction:

When electric current flows through a wire, magnetic field is generated around the wire. The direction of the field is determined by Maxwell’s right hand rule. Two magnetic fields interact in such a way that opposite poles attract and vice versa.

A current carrying wire generates a magnetic field around the wire the direction of which can be found by Maxwell’s right hand rule. It states that when the thumb points towards the direction of the current the right hand fingers represent the direction of the magnetic field. The two wires carrying current in opposite direction will generate magnetic fields in the same direction as determined by the right hand rule. Hence, the magnetic field will be large anywhere between the two parallel wires.

Conclusion:

The magnetic field will be large anywhere between the two parallel wires.

a.

To determine

The point where the magnetic field will be twice as large as from one wire.

Explanation of Solution

Introduction:

When electric current flows through a wire, magnetic field is generated around the wire. The direction of the field is determined by Maxwell’s right hand rule. Two magnetic fields interact in such a way that opposite poles attract and vice versa.

A current carrying wire generates a magnetic field around the wire the direction of which can be found by Maxwell’s right hand rule. It states that when the thumb points towards the direction of the current the right hand fingers represent the direction of the magnetic field. The two wires carrying current in opposite direction will generate magnetic fields in the same direction as determined by the right hand rule. Hence, the magnetic field will be twice as large along a line equidistant from the wires.

Conclusion:

The magnetic field will be twice as large along a line equidistant from the wires.