Question

Two parallel long wires A and B carry currents I₁ and I₂. (I₂ < I₁) when I₁ and I₂ are in the same direction the mag. field at a point mid way between the wires is 10 μT. If I₂ is reversed, the field becomes 30μT. The ratio (I₁/I₂) is ______ 

(a) 1 

(b) 2 

(c) 3 

(d) 4

Answer 1

 The correct option (b) 2

Explanation:

when I₁ & I₂ are in same direction, B = 10μT

∴   [(μ₀I₁)/(2πr)] – [(μ₀I₂)/(2πr)] = 10μT (1)

when I₁ & I₂ are in opposite direction B' = 30μT

∴ [(μ₀I₁)/(2πr)] + [(μ₀I₂)/(2πr)] = 30μT   (2)

(1) + (2) gives,

[(μ₀I₁)/(2πr)] = [(40μ₀T)/(2)] = 20μ₀T    (3)

(1) – (2) gives,

– [(2μ₀I₂)/(2πr)] = – 20μ₀T

i.e. [(μ₀I₂)/(2πr)] = 10μT (4)

Taking ratio of (3) & (4) gives

(I₁/I₂) = [(20μT)/(10μT)] = 2.