Magnetic Effects & Magnetism

JEE Main level, single correct, medium

48 of 276

Question 48 of 276

The electric current in a circular coil of four turns produces a magnetic induction 32T32T 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 :

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Answer: (C) 2T2T

Magnetic field at the centre of the coil is given by, B=μ0i2RB=\dfrac{{\mu }_{0}i}{2R}.
Now in the first case:
B=4(μ0i2R)B=4\left(\dfrac{{\mu }_{0}i}{2R}\right)
and for the second case:
B′=μ0i2R′B'=\dfrac{{\mu }_{0}i}{2R'}.
As the length of the wire will remain same, therefore
2πR′=4(2πR)⇒R′=4R2\pi R'=4\left(2\pi R\right) \Rightarrow R'=4R
Hence, required ratio will be
B′B=R4R′=116\dfrac{B'}{B}=\dfrac{R}{4{R}^{'}}=\dfrac{1}{16}
⇒B′=2T\Rightarrow B'=2T

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