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. `(8 N I mu_(0))/(5^(1//2) R)`
B. `(4 Nimu_(0))/(5^(3//2)R)`
C. `(4 NI mu_(0))/(5^(1//2)R)`
D. `(8 N I mu_(0))/(5^(3//2)R)`

Answer

d

Explanation

Magnetic field at an axial point due to circular current carrying loop.

Current in both coils are in the same direction so net magnetic field at point `P (x = R//2)` due to both coils will be added:
`B = ((2 mu_(0) NI (pi R^(2)))/(4 pi (R^(2) + R^(2)/4)^(3/2))) + ((2mu_(0)NI(pi R^(2)))/(4 pi (R^(2) + R^(2)/4)^(3/2)))`
` = 2 ((2 mu_(0)NI(pi R^(2)))/(4 pi (R^(2) + R^(2)/4)^(3/2))) = ((4 mu_(0)NI(pi R^(2)))/(4 pi (R^(2) + R^(2)/4)^(3/2)))= (8 mu_(0)NI)/(5^(3//2)R) `
Hence option (d) is correct.