Figure. shows two parallel and coaxial loops. The smaller loop (radius r) is above the larger loop (radius R), by distance `x gtgt R`. The magnetic field due to current `i` in the larger loop is nearly constant throughout the smaller loop. Suppose that `x` is increasing at a constant rate of `dx//dt = v`.

Determine the magnetic flux through the smaller loop as a function of `x`.

Options

A. `(mu_(0)IR^(2)xxpir^(2))/((R^(2)+x^(2))^(3//2))`
B. `(mu_(0)IR^(2)xxpir^(2))/(2(R^(2)+x^(2))^(3//2))`
C. `(2mu_(0)IR^(2)xxpir^(2))/((R^(2)+x^(2))^(3//2))`
D. `(sqrt2mu_(0)IR^(2)xxpir^(2))/((R^(2)+x^(2))^(3//2))`

Answer

B