Question

Consider the following statements:

A current I flows through a circular coil of one turn of radius R in the counter-clokcwise direction.

1. The magnetic field at the centre is inversely proportional to R.

2. The magnetic moment of the coil is directly proportional to R².

3. The magnetic field at its centre is directly proportional to R².

Which of the above statements is/are correct?
1. 1 and 2
2. 1 only
3. 2 and 3
4. 3 only

Answer 1

Correct Answer - Option 1 : 1 and 2

Current (I) flows through a circular coil of radius R and only one turn, in a counter-clockwise direction.

Now, the magnetic field ‘H’ is given by

\(H = \frac{I}{{2\pi R}}\)

\( \Rightarrow H \propto \frac{1}{R}\) 

Magnetic moment (m) is given by

m = I π R² a_n ⇒ m ∝ R²

Therefore, the magnetic field at the centre is inversely proportional to the radius (R) and the magnetic moment (m) is directly proportional to R².