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 5 g and conducts a current downward. The acceleration due to gravity is 9.81 m/s2.
(a)What is the equilibrium angular displacement of the wire from vertical if the horizontal magnetic field is 0.07 T and the current is 0.35 A? Answer in units of ?.
(b)If the current is 25 A and a displacement from vertical of 0.3 mm can be detected for the free end, what is the horizontal magnetic field sensitivity of this gaussmeter?