Question

A coil having 9 turns carrying a current produces a magnetic field \( B_1 \) at the centre. Now the coil is rewound into 3 turns carrying the same current. Then the magnetic field at the centre \( B_2 \) is:

• A. \( \frac{B_1}{9} \)
• B. \( 3B_1 \)
• C. \( 2B_1 \)
• D. \( \frac{B_1}{3} \)

Answer 1

The Correct Option is A

The magnetic field at the center of a coil is directly proportional to the number of turns in the coil.
This relationship is given by the formula:\( B = \frac{\mu_0 N I}{2R} \) where: 
- \( N \) is the number of turns, 
- \( I \) is the current, 
- \( R \) is the radius of the coil. 

If the number of turns is reduced by a factor of 3, the magnetic field at the center will decrease by a factor of 9 (since \( B \propto N \)). 

Thus, if the original magnetic field is \( B_1 \), the new magnetic field after reducing the number of turns to 3 is:\( B_2 = \frac{B_1}{9} \)