Question

What is the direction of the field halfway between two horizontal parallel wires if the top wire has a current of 4 A to the left and the bottom wire has a current of 2 A to the right?
A) Out of the page
B) into the page
C) Left
D) The magnetic fields cancel out at that position

Answer 1

Answer:

A) Out of the page.

Explanation:

Right-hand rule points the direction of the magnetic field at any point.

Top wire: Current is to the left. Point your thumb to the left and curl your other fingers around the wire. The tips of the four fingers points the direction of the field at that point. In this case, out of the page.

Bottom wire: Current is to the right. Point your thumb to the right and curl your other fingers around the wire. The tips of the four finger points out of the page again.

So, the total field produced by both wires is directed out of the page.

Another method to figure out the direction is the mathematical method.

Use the B-field formula:

$d\vec{B} = \frac{\mu_0}{4\pi}\frac{Id\vec{l}\times \^r}{r^2}$

The cross product between the direction of the current and the target position gives the direction of the B-field. If the left is -x direction and downwards is the -y direction, then

$(-\^x) \times (-\^y) = +\^z$ for the top wire.

$(+\^x) \times (+\^y) = +\^z$ for the bottom wire.