A Helmholtz coil has a pair of loops, each withN turns and radius R. They are placed coaxially at distance R and the same current I flows through the loops in the same direction. The magnitude of magnetic field at P, midway between the centres A and C, is given by [Refer to figure given below]:

Options

A. `(4Nmu_(0)I)/(5^(1//2)R)`
B. `(4Nmu_(0)I)/(5^(3//2)R)`
C. `(8Nmu_(0)I)/(5^(3//2)R)`
D. `(8Nmu_(0)I)/(5^(1//2)R)`

Answer

C

Explanation

Required magnetic fieldis given by `B=2((mu_(0)NIR^(2))/(2(R^(2)+(R^(2))/4)^(3//2)))=(mu_(0)NIR^(2))/(5^(3//2)/8)=(8mu_(0)NI)/(5^(3//2)R)`