Question

A straight wire is aligned east-west in a region where Earth’s magnetic field has magnitude 0.0780 mT and direction 67.1° below the horizontal, with the horizontal component directed due north. The wire carries a current I toward the west. The magnetic force on the wire per unit length of wire has magnitude 0.0300 N/m.
(a) What is the direction of the magnetic force on the wire?
(b) What is the current I?

Answer 1

Explanation:

It is given that,

Earth's magnetic field, $B=0.078\ mT=0.078\times 10^{-3}\ T$

Direction of magnetic field, 67.1 degrees below the horizontal, with the horizontal component directed due north.

The magnetic force on the wire per unit length of wire, $\dfrac{F}{L}=0.0300\ N/m$

(a) The given scenario is shown in the attached figure as :

Using the right hand rule to find the direction of magnetic force on the wire. By using this rule, we get the magnetic force acting on the wire is in upward direction.

(b) Let I is the current flowing in the wire. The magnetic force is given by the following formula as:

$F=ILB$

$I=\dfrac{F}{LB}$

$I=\dfrac{0.0300}{0.078\times 10^{-3}}$

I = 384.61 A

Hence, this is the required solution.