JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Magnetic Effects of Current

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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)8 T
(B)4 T
(C)2 T✓ Correct
(D)16 T

Answer: (C)

Solution

At the centre of a coil of

n

turns and radius

R

B = \frac{μ _{0} ni}{2 R}

, and the four-turn coil gives

32

T. Rewinding the same length of wire into a single turn makes its circumference four times larger, so

2 π R^{'} = 4 (2 π R)

and

R^{'} = 4 R

. The new field is

B^{'} = \frac{μ _{0} i}{2 ( 4 R )} = \frac{μ _{0} i}{8 R}

, and taking the ratio to the original,

\frac{B ^{'}}{B} = \frac{μ _{0} i /8 R}{4 μ _{0} i /2 R} = \frac{1}{16}

, so

B^{'} = \frac{32}{16} = 2

JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Single correct option

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JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Magnetic Effects of Current

Solution

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