A simple gaussmeter for measuring horizontal magnetic fields consists of a stiff

Question

A simple gaussmeter for measuring horizontal magnetic fields consists of a stiff 60 cm wire that hangs 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 1 g and conducts a current downward. What is the equilibrium angular displacement of the wire from vertical if the horizontal magnetic field is 0.04 T and the current is 0.20 A? If the current is 20 A and a displacement from vertical of 0.5 mm can be detected for the free end, what is the horizontal magnetic field sensitivity of this gaussmeter?

Explanation / Answer

a)At equilibium, mg sin(theta)=ILB sin(theta)=0.2A*0.42m*0.04T/0.001kg/9.81 theta=20 deg b) sin (theta)=0.0005m/0.42m=0.00119 rad, B=0.00119*0.001kg*9.81/0.42m/20A=1.39*10^(-6) T= 1.39 micro T

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