Question:
A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L ( L > > l)$ . The loops are coplanar and their centres coincide . The mutual inductance of the system is proportional to
A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L ( L > > l)$ . The loops are coplanar and their centres coincide . The mutual inductance of the system is proportional to
Updated On: Jul 6, 2022
- $l / L$
- $l^2/L$
- $L / l$
- $L_2/l$
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The Correct Option is B
Solution and Explanation
Magnetic field produced by a current $i$ in a large square loop at its centre
$B \propto \frac{i}{L}$ say $B = K \frac{i}{L}$
$\therefore$ Magnetic flux linked with smaller looop,
$\phi = B.S$ $\phi = \left( K \frac{i}{L} \right) ( l^2)$
Therefore, the mutual inductance
$M = \frac{\phi}{i} = K \frac{l^2}{L}$ or $M \propto \frac{l^2}{L}$
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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