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)/(2√2)`	`("B"_0)/(5√5)`	`("B"_0)/(10√10)`

Answer 1

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

B = `μ_0/(4pi) (2"NI"(pi"a"^2))/"r"^3`, for N turns

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

At the center, x = 0: = `μ_0/2 "I"/"a"`

At x = a: = `("B"_0)/(2√2)`

At x = 2a: `("B"_0)/(5√5)`

At x = 3a: `("B"_0)/(10√10)`