Question

A long straight wire of circular cross section of radius 'a' carries a steady current I. The current is uniformly distributed across its cross section. The ratio of magnitudes of the magnetic field at a point `a/2` above the surface of wire to that of a point `a/2` below its surface is ______.

विकल्प

• 4 : 1

• 1 : 1

• 4 : 3

• 3 : 4

Answer 1

A long straight wire of circular cross section of radius 'a' carries a steady current I. The current is uniformly distributed across its cross section. The ratio of magnitudes of the magnetic field at a point `a/2` above the surface of wire to that of a point `a/2` below its surface is 4 : 3.

Explanation:

At P₂, B₂ = `(mu_0I)/(2pi((3a)/2)) = (mu_0I)/(3pia)`

At P₁, B₁ = `(mu_0(I//4))/(2pi(a//2)) = (mu_0I)/(4pia)`

`therefore B_2/B_1 = (((mu_0I)/(3pia)))/(((mu_0I)/(4pia))) => B_2/B_1 = 4/3`