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 $9 \sqrt{3}$
- Increases by a factor of 3
- Decreases by a factor of 9
- Increases by a factor of 27
The Correct Option is B
Solution and Explanation
Total length L will remain constant
\(L = (3a) N\) (N = total\, turns)
and length of winding (\(l\))= \((d) N\) (d = diameter of wire)
Self inductance = \(\mu_o n^2 Al= \mu_o n^2(\frac{\sqrt3 }4 a^2)dN\)
Self inductance (L) ∝ \(a^2N\)
As \(N = \frac{l}{3a} \rightarrow N ∝\frac1{a}\)
\(\therefore L ∝a\)
So, as a is increased to 3a the Self inductance will be 3 times.
Hence, the correct answer is option (B): Increases by a factor of 3
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Concepts Used:
Electromagnetic Induction
Electromagnetic Induction is a current produced by the voltage production due to a changing magnetic field. This happens in one of the two conditions:-
- When we place the conductor in a changing magnetic field.
- When the conductor constantly moves in a stationary field.
Formula:
The electromagnetic induction is mathematically represented as:-
e=N × d∅.dt
Where
- e = induced voltage
- N = number of turns in the coil
- Φ = Magnetic flux (This is the amount of magnetic field present on the surface)
- t = time
Applications of Electromagnetic Induction
- Electromagnetic induction in AC generator
- Electrical Transformers
- Magnetic Flow Meter