Show that the expression for the magnetic field of a toroid reduces to that for the field of an infinite solenoid in the limit that the central radius goes to infinity.

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Show that the expression for the magnetic field of a toroid reduces to that for the field of an infinite solenoid in the limit that the central radius goes to infinity.

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Step 1

 

Here we know that the magnetic field inside a toroid is not uniform, it varies inversely proportional to the distance R from the axis and it is written as;

B=μNR22(R2+X2)32 ----(1)

Here, N is the number of turns.

' I ' is the current.

R is the distance.

Step 2

For net magnetic field the integration of magnetic field goes to infinity is written as;

Bnet = -+BndxPutting the values of B we have;Bnet = -+μoIR22(R2+X2)32ndx         = μoIR22n-+1(R2+X2)32dx         = μoIR22n xR2(R2+X2)12-+

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