Question

When a certain length of wire is turned into one circular loop, the magnetic induction at the centre of coil due to current 'I' flowing through it is B₁. If the same wire is turned into four loops to make a circular coil, the magnetic induction at the centre of this coil is 'B₂' for same current then relation between B₂ and B₁ is ____________.

Options

• B₂ = 8B₁

• B₂ = 16 B₁

• B₂ = 4B₁

• B₂ = 64 B₁

Answer 1

When a certain length of wire is turned into one circular loop, the magnetic induction at the centre of coil due to current 'I' flowing through it is B₁. If the same wire is turned into four loops to make a circular coil, the magnetic induction at the centre of this coil is 'B₂' for same current then relation between B₂ and B₁ is B₂ = 16 B₁.

Explanation:

The magnetic induction at the centre or the coil is given by

`"B" = (mu_0 "nI")/(2"r")`

When the same length of wire is turned into four loops, the number of turns will become four times and the radius will become one-fourth. Hence B will become 16 times.

`therefore "B"_2/"B"_1 =16`