Question

The mag. field due to a current carrying circular Loop of radius 3cm at a point on the axis at a distance of 4cm from the centre is 54μT what will be its value at the centre of the LOOP. 

(a) 250μT 

(b) 150μT 

(c) 125μT 

(d) 75μT

Answer 1

The correct option (a) 250 μT 

Explanation:

mag field at distance x from centre of coil is

B = [(μ₀R²I)/{2(R² + x²)^3/2}]

at the centre x = 0 hence B = (μ₀I/2R) (1)

at distance x = 4cm, B = 54Μt  also R = 3cm

hence

54 × 10^–6 = [(μ₀R²I)/{2(R² + 4²)^3/2}]

∴  54 × 10^–6 = [(μ₀R²I)/{2(3² + 4²)^3/2}]

∴  [{(54 × 10^–6 × 2 × (5²)^3/2}/3²] = μ₀­I

∴  μ₀I = 12 × 10^–6 × 5³

from (1),

B = (μ₀I/2R) = [(12 × 10^–6 × 125)/(2 × 3)]

B = 250 × 10^–6 T

∴  B = 250 μT