Question

The magnetic field developed due to current carrying coil at its centre is $B$. If the new coil of two turns is prepared from the above coil and same current is passed, then the magnetic field at the centre of the new coil will be

• A. $\dfrac{B}{2}$
• B. $4B$
• C. $\dfrac{B}{4}$
• D. $2B$

Hint:

When the same wire is reshaped into more turns, the radius decreases, greatly increasing the magnetic field.

Answer 1

The Correct Option is B

Step 1: Magnetic field at the centre of a circular coil.
The magnetic field at the centre of a coil is given by: \[ B = \dfrac{\mu_0 n I}{2r} \] where $n$ is number of turns and $r$ is radius of the coil.
Step 2: Effect of making a new coil of two turns.
When the same wire is used to make two turns, the radius of each turn becomes half of the original radius.
Step 3: Compare magnetic fields.
For new coil: \[ B' = \dfrac{\mu_0 (2) I}{2 (r/2)} = \dfrac{2\mu_0 I}{r} \] Step 4: Express new field in terms of $B$.
Original field: \[ B = \dfrac{\mu_0 I}{2r} \] \[ B' = 4B \]