Question

A long straight wire of radius "a" carries a steady current I the current is uniformly distributed across its cross-section. The ratio of the magnetic field at a/2 and 2a is ____

(a) (1/4)

(b) 4

(c) 1

(d) (1/2)

Answer 1

The correct option (c) 1

Explanation:

∵ B = [{(μ0I)/(2πa2)} ∙ r]

for r = (a/2),

B = [(μ0I)/(2πa2)] × (a/2) = [(μ0I)/(4πa)] (inside the wire)

B' = [(μ0I)/(2πr)]

for r = 2a, B' = [(μ0I)/(2π × 2a)] = [(μ0I)/(4πa)] (outside the wire)

∴ B = B'

Hence the ratio is 1.