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?

Answer 1

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.