You know that two infinite sheets of opposite charge can be used to create a uni

Question

You know that two infinite sheets of opposite charge can be used to create a uniform electric field (for points between the two sheets) and you know that two infinite arrays of opposite current carrying wires can produce a uniform magnetic field (for points between the two arrays), but there is another possibility. Recall that two large circular coils with N tightly wound turns of radius Rcan also yield a uniform magnetic field. If the two coils are separated by a distance R, where along the horizontal x-axis is the magnetic field uniform, and what additional calculations will you need to perform to prove that the field at this location is indeed uniform?

Explanation / Answer

The magnetic feild of the coil is given by

B=(u0NIR2) / 2(x2+R2)3/2

Now ,the magnetic feild due to the two coils be B1 and B2. The total magnetic feild is

B=B1+B2

The magnetic feild wil be uniform when ever the sepration between two coils is equal to the radius of the coil.

B=B1+B2

B= u0NIR2 /( ( 0.5d-x)2 + R2)3/2 x(unitvector) + u0NIR2 /( (0.5d+x)2 + R2)3/2( x unitvector)

putting the value fo x=0 in the above equation we will get the magnetic feild uniform feild between the coils at its centre.

B= u0NIR2 / (R2 + R2)3/2 x ( unit vector) + u0NIR2 / (R2 + R2)3/2 ( x unit vector)

B= u0NIR2 / (2R2)3/2 x ( unitvector) + u0NIR2 / (2R2)3/2   ( x unit vector)

B= 2(u0NIR2 / (2R2)3/2) x ( unit vector)

B= 2(u0NIR2 / 23 R3)

B= u0NIR2 / 4R3

B=u0NI/ 4R         This will be the magnitic feild on the central points between two coils.

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