Question

A conducting loop of resistance R and radius r has its centre at the origin of the coordinate system in a magnetic field of induction B. When it is rotated about y-axis through 90°, the net charge flown in the loop is directly proportional to:

Options

• R^-1

• R

• r²

• r

Answer 1

r²

Explanation:

Apply 2^nd law of electromagnetic induction

ε = `("d"phi)/"dt" ⇒  int_(phi_1)^(phi_2) d phi = Delta phi = int epsilon "dt"` 

The total charge flown in the loop q = `int`Idt

or q = `int epsilon/"R""dt" = (Delta phi)/"R" = ("B"pi"r"^2)/"R" `

i.e. q ∝ B, q ∝ r², and q ∝`1/"R"`