A nonconducting sphere has mass 75.2 g and radius 21.2 cm. A flat, compact coil

Question

A nonconducting sphere has mass 75.2 g and radius 21.2 cm. A flat, compact coil of wire with four turns is wrapped tightly around it, with each turn concentric with the sphere. The sphere is placed on an inclined plane that slopes downward to the left (see figure below), making an angle theta with the horizontal so that the coil is parallel to the inclined plane. A uniform magnetic field of 0.351 T vertically upward exists in the region of the sphere. (a) What current in the coil will enable the sphere to rest in equilibrium on the inclined plane? (b) Show that the result does not depend on the value of theta. (Use the following as necessary: M for the mass of the sphere, N for the number of turns, B for the magnitude of the magnetic field, and R for the radius of the sphere, g, and pi.)

Explanation / Answer

I = m*g*r/N*A*B

= m*g*r/N*pi*r^2*B

= m*g/N*pi*r*B

= 75.2*10^-3*9.8/4*pi*(21.2*10^-2)*0.351

= 0.788 A

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