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A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil:
- decreases by a factor of 9√3
- increases by a factor of 27
- decreases by a factor of 9
- increases by a factor of 3
Correct answer: increases by a factor of 27
Solution
When the linear dimensions of the coil are increased by a factor of 3, the area enclosed by the coil increases by a factor of 9 (since area scales with the square of the linear dimensions), and the number of turns per unit length remains constant. The self-inductance is proportional to the area and the square of the number of turns, leading to an overall increase by a factor of 27.
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