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Question

# A circular coil connected to a cell of e.m.f E produced a magnetic field. The coil is unwound, stretched to double its length, rewound into a coil of 13 of the original radius and connected to a cell of e.m.f E1 to produce the same field at the centre. Then E1 is :

A
E2
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B
2E3
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C
9E4
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D
E6
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Solution

## The correct option is D 2E3Let initial length is L and Area of cross-section of wire is A. Consider L and A are the length and area after stretching.Then, volumeof wire must remain same, i.e. A′L=AL′A′L=2ALA′=A2Therefore,RiRf=LAA.L=14 Where Ri and Rf are initial and final resistanceOr, Rf=4RiAssuming the number of turns are also doubled by stretching the length and circumference of coil is sufficient to accommodate even after the coil radius is reduced to 13 of original radiusNow,Magnetic field at the center of the coil is same. Therefore,Ir=6Ifr Where I and If are initial and final currentOr,I=6IfEE1=IRiIfRf=32Or, E1=2E3

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