Question

The researcher requires the force on the wire to point upward with a magnitude of 4.2x10-4 N. The length of the wire that is in the field is 50 mm, and the wire carries a current of 30 mA from left to right. What direction and magnitude of magnetic field will provide the necessary force?

Answer 1

Answer:

The magnetic force can be found by using the following equation:

$F_B = IL\times B$

Let’s first deal with the magnitude, then we will figure out the direction by using the right hand rule.

$4.2\times 10^{-4} = (30\times 10^{-3})\times (50\times10^{-3}) \times B\\4.2 \times 10^{-4} = 1500 \times 10^{-6}\times B\\(28\times 10^{-4})\times 10^2 = B\\B = 28\times 10^{-2}$

The direction of the L is equal to the direction of the current. So, the direction of the L is to the right. The required force is to be pointed upward.

By the right hand rule the magnetic field should be directed towards ‘into the plane’.

Explanation:

In the questions regarding the magnetic field, the cross product and the directions of the vectors are crucial. So, you should use right-hand rule efficiently.

Right-hand rule: $A \times B = C$

Point your four fingers (except the thumb) towards the same direction as A.

Point your palm towards the same direction as B.

Your thumb should show the direction of C.