Question

A circular loop of radius 0.3 cm lies parallel to much bigger circular of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with the bigger loop is ______.

Options

• 3.3 × 10^-11 weber

• 6 × 10^-11 weber

• 6.6 × 10^-9 weber

• 9.1 × 10^-11 weber

Answer 1

A circular loop of radius 0.3cm lies parallel to much bigger circular of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with the bigger loop is 9.1 × 10^-11 weber.

Explanation:

Let flux linked with smaller loop is Φ₁ and with bigger loop is Φ₂.

Given R₂ = 0.2 m

R₁ = 0.003 m

x = 15 cm = 0.15 m

Now Φ₁ = B₂ A₁

`= mu_0/(4pi) [(2pi " R"_2^2 " I"_2)/("R"_2^2 + x^2)^(3//2)] pi"R"^2_1`

M = `phi_1/"I"_2 = mu_0/(4pi) (2pi " R"_2^2 pi " R"_1^2)/("R"_2^2 + x^2)^(3//2)`

Now Φ₂ = M I₁ 

`= mu_0/(4pi)  (2pi " R"_2^2 pi " R"_1^2)/("R"_2^2 + x^2)^(3//2)*"I"_1`

= 9.1 × 10^-11 weber