Question

Pick out the expression for magnetic field inside a toroid from the following.

(a) B = μ0 NI

(b) B = 2μ0 NI

(c) B = \(\frac {\mu_o}{NI}\)

(d) B = \(\frac {\mu_o N}{I}\)

I got this question during an online exam.

Asked question is from Solenoid and Toroid in chapter Moving Charges and Magnetism of Physics – Class 12

Answer 1

Right answer is (a) B = μ0 NI

For explanation: Ampere’s circuital law:

∮ B.dl = ∮ B.dlcos⁡0 = B ∮ dl = B.2πr  …………………..1

But, for a toroid:

∮ B.dl = μ0 × total current threading the toroid

∮ B.dl = μ0 × total number of turns in the toroid × I

∮ B.dl = μ0 N2πrI ……………………………2

From 1 and 2

B.2πr = μ0 N2πrI

Therefore, B = μ0NI