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  4. A coil is wound on a frame of rectangular cross-section. If all the linear dimensional frame are increased by a factor of 2 and the number of turns per unit length of the coil remains the same, self-inductance of the coil increases by a factor of

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Q. A coil is wound on a frame of rectangular cross-section. If all the linear dimensional frame are increased by a factor of 2 and the number of turns per unit length of the coil remains the same, self-inductance of the coil increases by a factor of

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Solution:

From the relation $ L={{\mu }_{0}}{{n}^{2}}Al $ If all the dimensions of the frame are increased by a factor of 2, then area is increased by a factor of 4 and length by a factor of 2. Hence, L becomes 8 times.