Question

A student records the following data for the magnitudes (B) of the magnetic field at axial points at different distances x (See figure given below) from the centre O of a circular coil of radius a carrying a current I. Verify (for any two) that these observations are in good agreement with the expected theoretical values of B.

X	x = 0	x = a	x = 2a	x = 3a
B	B0	`(B_0)/(2sqrt2)`	`(B_0)/(5sqrt5)`	`(B_0)/(10sqrt10)`

Answer 1

The expression for B at an axial point of a circular coil carrying current is,

B = `mu_0/(4 pi) (2 NI(pi a^2))/r^3`, for N turns

B = `μ_0/(4 pi) (2 I(pi a^2))/r^3`, for N = 1 turn

At the center, x = 0: = `μ_0/2 I/a`

At x = a: = `(B_0)/(2 sqrt 2)`

At x = 2a: `(B_0)/(5 sqrt 5)`

At x = 3a: `(B_0)/(10 sqrt 10)`