The radius of a circular current carrying coil is R At what distance from the centre of the coil - Physics - Moving Charges And Magnetism

Question

The radius of a circular current carrying coil is R At what
distance from the centre of the coil on its axis, the intensity of
magnetic field will be 1/2root2 times that at the centre?

Sushant · Accepted Answer

hi 
Neha,

Please find below the solution to the asked query:

magnetic fiels along the axis of a circular current carrying coil is :μoiR22(x2+ r2)3/2magnetic field at the center = μoi2Rgiven μoiR22(x2+ R2)3/2 = 122μoi2Ror,R2(x2+ R2)3/2 = 122Ror  22R3 = (x2+ R2)3/2or, 8R6 =  (x2+ R2)3or, 2R2 = x2 +R2or x = ± 2R2 -R2 = ±Ranswer

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The radius of a circular current carrying coil is R. At what distance from the centre of the coil on its axis, the intensity of magnetic field will be 1/2root2 times that at the centre?