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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

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Answer:

Angular displacement of the wire is 0.5 degree with the vertical

Explanation:

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

so we will have

[tex](iLB)(\frac{L}{2}cos\theta) = mg(\frac{L}{2} sin\theta)[/tex]

so we have

[tex]\frac{iLB}{mg} = tan\theta[/tex]

so we have

[tex]tan\theta = \frac{0.1(0.50)(0.01)}{(6 \times 10^{-3})9.81}[/tex]

so we have

[tex]tan\theta = 8.5 \times 10^{-3} [/tex]

[tex]\theta = 0.5 degree[/tex]

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