Question

A flat circular coil of 70 turns has a diameter of 20 cm and carries a current of 5 A. Find the magnitude of the magnetic induction at a point on the axis 20 cm from the centre of the coil.

Answer 1

Data: N = 70, R = 10 cm = 0.1 m, I = 5 A, z = 0.2 m and μ₀ = 4π × 10⁻⁷ T.m/A

Using, B = `((μ_0)/(4π)) (2NIA)/((R^2 + z^2)^(3/2))`

i.e., `(R^2 + z^2)^(3/2) = [(0.1)^2 + (0.2)^2]^(3/2)`

= `(0.01 + 0.14)^(3/2)`

= `(5 xx 10^-2)^(3/2)`

log 125 = 2.0969
                     `underline(× 1/2)`

                 1.0484
antilog (1.0484) = 11.18

= `sqrt(125 xx 10^-6)`

= `sqrt125 xx 10^-3`

= 1.118 × 10⁻² m³

But, A = πR² = 3.142 (0.1)² = 3.142 × 10⁻² m²

∴ B = `((10^-7) (2) (70) (5) (3.142 xx 10^-2))/(1.118 xx 10^-2)`

= `(7 xx 3142 xx 10^-5)/1.118`

= 1.967 × 10⁻⁴

T = 196.7 μT