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 :

Solution

Physics sir · 3 steps

The wire length stays fixed, so one turn means four times the radius. Both changes cut B.

1. Field at centre. For a circular coil of N turns and radius r, the field at the centre is B = (μ₀ N I)/2r. The current I is unchanged, so B ∝ N/r.
2. Same wire length. Rewinding does not change the wire, so N × 2π r stays the same. With 4 turns of radius r, the length is 8π r. A single turn of the same wire therefore has radius 4r.

   B'/B = (N'/r')/(N/r) = (1/(4r))/(4/r) = 1/16

3. So. B' = 32/16 = 2 T, which is option (a).

The idea to keep. When a wire is rewound, N r stays constant, so B ∝ N/r becomes B ∝ N². Halve the turns and the centre field drops to a quarter.

Answer from the NTA final answer key. Solution by PrepWiser.