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Magnetic field on the axis of a circular coil
B1=2(R2+z2)3/2μ0iR2
Magnetic field at the center of the circular coil:
B2=2Rμ0i
Given, B1=81B2
⇒2(R2+z2)3/2μ0iR2=812Rμ0i
⇒8R3=(R2+z2)3/2
⇒64R6=(R2+z2)3
(4R2)3=(R2+z2)3
⇒4R2=R
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