Question

A coil of one turn is made of a wire of certain length and then from the same length, a coil of two turns is made. If the same current is passed in both the cases, then the ratio of the magnetic inductions at their centres will be:

Options

• 2 : 1

• 1 : 4

• 4 : 1

• 1 : 2

Answer 1

1 : 4

Explanation:

Let ℓ be the length of the wire.

1st case: ℓ = 2πr ⇒ r = `ℓ/(2π)`

B = `(μ_0"I")/(2π"r") = (μ_0"I")/ℓ`

2nd case: ℓ = 2(2πr') ⇒ r' = `ℓ/(4π)`

B' = `(μ_0"In")/(2πℓ/(4π)) = (2μ_0"I")/(ℓ/2)` ....(where n = 2)

on putting the value of B ⇒ B' = `4((μ_0"I")/"l")` = 4B