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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»

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



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