Consider the toroidal configuration of current shown. The innerradius of the tor

Question

Consider the toroidal configuration of current shown. The innerradius of the toroid is a and the outer radius of the toroid is b . The thickness of the toroid is(b-a). The current in the wire is I and there are N turns of wire around the device. The corematerial of the toroid has a permeability . Answer the following in terms of quantities givenand relevant physical constants or a subset thereof

(a) Using Ampere’s law along the appropriate path what compute the magnetic field for r < a(b) Using Ampere’s law along the appropriate path what compute the magnetic field for r >b.(c) Using Ampere’s law along the appropriate path compute the magnetic field fora > r > b .

Explanation / Answer

B.dl = 0 ienclosed

take an amperian loop to be path1.

ienclosed = 0 >>>>> By Ampere’s law, the value of the integral is zero as no current is enclosed by the loop.

>>> for r<a : B = 0

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b)

B.dl = 0 ienclosed

take an amperian loop to be path3.

>>>> B(2r) = 0 ienclosed

>>>> B(2r) = 0 (N i) >>>> B = 0Ni / 2r

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c)

B.dl = 0 ienclosed

take an amperian loop to be path3.

ienclosed = 0 >>>>> By Ampere’s law, the value of the integral is zero as no net current is enclosed by the loop.

>>>>> for r>b : B = 0

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