A non - conducting sphere has mass of 100 g and radius 20 cm . A flat compact coil of wire with turns 5 is wrapped tightly around it with each turns concentric with the sphere. This sphere is placed on an inclined plane such that plane of coil is parallel to the inclined plane.
A uniform magnetic field of `0.5` T exists in the region in vertically upwards direction. Compute the current I required to rest the sphere in equilibrium.
` (##SUR_PHY_XII_V01_C03_E04_005_Q01##) `

Explanation

At equilibrium
` f_(s) R - p_(m) " B sin " theta = 0`
mgR = NBAI
I`= ("mg R")/("NBA") = ("mgR")/("NB"pi R^(2)) `
I = `(mg )/(pi R "NB") `
Mass of the sphere, m = 100 g = 100 `xx 10^(-3)` kg
Radius of the sphere R = 20 cm = `20 xx 10^(-2) ` m
Number of turns n = 5
Uniform magnetic field B = 0.5 T
I = `(100 xx 10^(-3) xx 10)/(pi xx 20 xx 10^(-2) xx 5 xx 0.5) = (1000 xx 10^(-3))/(pi xx 50 xx 10-2) = (20 xx 10^(-4))/(pi )`
I = `(2)/(pi ) ` A