If (B₁ ) is the magnetic field induction at a point on the axis of a circular coil of radius (R ) situated at a distance (R 3 ) and (B₂ ) is the magnetic field at the centre of the coil, then the ratio of ( B₁ B₂ ) is equal to

Step-by-step solution

According to question, (B₁= ₀ I R^2 2 (R^2+r^2 )^ 3 / 2 ) Here, ( r=R 3 ) ( aligned B₁ & = ₀ I R^2 2 [R^2+(R 3 )^2 ]^ 3 / 2 = ₀ I R^2 2 [4 R^2 ]^ 3 / 2 = ₀ I R^2 16 R^3 B₁ & = ₀ I 16 R (i) aligned ) and ( B₂= ₀ I 2 R ) ...(ii) [magnetic field at centre] Now, dividing Eq. (i) by Eq. (ii), we get ( B₁ B₂ = ₀ I / 16 R ₀ I / 2 R = 1 8 )