Question

There are 3 vertical parallel straight wires. The wire to the left has a current flowing vertically up, the wire in the middle has a current vertically up, the wire to the right has a current vertically down. (It helps to draw a picture of this.) What is the direction of the total magnetic force on the wire in the middle

Answer 1

Answer:

The net force on the middle wire will be zero.

Explanation:

Given:

There are three vertical wires. The wires to the left and in the middle have a current flowing vertically up and the wire to the right has a current vertically down.

Consider the figure shown. Let's assume that the magnitude of current in each wire is $I$ and each wire is situated at a distance $r$ from each other.

The magnetic field on the middle wire due to the wire in left is directed perpendicularly inward to the screen, as shown in the diagram. The magnetic field on the middle wire due to the wire in the right is directed perpendicularly outward to the screen, as shown in the diagram.

The force on the wire in the middle due to the left one is given by

$F_{21} = \dfrac{\mu_{0}I^{2}}{2 \pi r}$

where $\mu_{0}$ is the permeability of free space.

The direction of the force is towards the wire in the left, as shown in the figure.

The force on the wire in the middle due to the right one is given by

$F_{23} = \dfrac{\mu_{0}I^{2}}{2 \pi r}$

The direction of the force is towards the wire in the right, as shown in the figure.

As the magnitude of the forces are equal but the directions are opposite to each other, the net force on the middle wire will be zero.