Moving Charges and Magnetism Problems - Numerical 07

A given length L of a uniform wire is bent (i) into a single circular turn and (ii) into n identical circular turns. What is the ratio of the magnetic field at the center of the coil in both the cases mentioned above when same current is passed through them?

Sub Topics

Suggested solution:

Suggested solution:

Let r₁ be the radius of the circular coil of one turn and B₁ be the magnetic field at it's center due to current i.

Then,

2 r₁ = L or r₁ = L/2 and B₁ = m_onI / 2r₁ = 2n² m_oI / L

Let r₂ be the radius of each turn when the wire is bent into a circular coil having n turns. Also B₂ is the magnetic field at the center due to the current I.

Now,

(2 r₁) n = L or r₁ = L/2n and B₂ = m_on I / 2r₁ = 2 m_on I / l

From equations (1) and (2), we get

B₁ / B₂ = 1/n