Question

A simple gaussmeter for measuring horizontal magnetic fields consists of a stiff 50 cm wire that hangs vertically from a conducting pivot so that its free end makes contact with a pool of mercury in a dish below. The mercury provides an electrical contact without constraining the movement of the wire. The wire has a mass of 6 g and conducts a current downward. The acceleration due to gravity is 9.81 m/s 2 . What is the equilibrium angular displacement of the wire from vertical if the horizontal magnetic field is 0.01 T and the current is 0.1 A

Answer 1

Angular displacement of the wire is 0.5 degree with the vertical

Step-by-step explanation:

At equilibrium the torque due to gravity is balanced by the torque due to magnetic force on the wire

so we will have

`(iLB)((L)/(2)cos\theta) = mg((L)/(2) sin\theta)`

so we have

`(iLB)/(mg) = tan\theta`

so we have

`tan\theta = (0.1(0.50)(0.01))/((6 * 10^(-3))9.81)`

so we have

`tan\theta = 8.5 * 10^(-3)`

`\theta = 0.5 degree`