Question

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :

• A. 16 T
• B. 2 T
• C. 8 T
• D. 4 T

Answer 1

The Correct Option is B

The magnetic field \( B \) is initially given by the equation:

Step 1: \( B = \frac{\mu_0 i}{2R} \times 4 \), which is the original magnetic field expression.

Step 2: For the new radius \( R' = 4R \), the new field \( B' \) is given by:

Step 3: Substitute \( R' \) into the magnetic field formula: \( B' = \frac{\mu_0 i}{2R'} = \frac{\mu_0 i}{8R} \).

Step 4: Now, calculate the ratio \( \frac{B'}{B} = \frac{1}{16} \), indicating that the new magnetic field is \( \frac{1}{16} \) of the original field.

Step 5: With this ratio, we conclude that the new magnetic field \( B' \) is \( 2T \).