Question:
A short solenoid of radius $a$, number of turns per unit length $n_{1}$ and length $L$ is kept coaxially inside a very long solenoid of radius $b$, number of turns per unit length $n_{2}$. What is the mutual inductance of the system?
A short solenoid of radius $a$, number of turns per unit length $n_{1}$ and length $L$ is kept coaxially inside a very long solenoid of radius $b$, number of turns per unit length $n_{2}$. What is the mutual inductance of the system?
Updated On: May 15, 2024
- $\mu_{0} \,\pi \,b^{2} \,n_{1} \,n_{2} \,L$
- $\mu_{0}\, \pi \,a^{2} \,n_{1}\, n_{2}\, L^{2}$
- $\mu_{0} \,\pi \,a^{2} \,n_{1}\, n_{2}\, L$
- $\mu_{0}\, \pi\, b^{2} \,n_{1}\, n_{2}\, L^{2}$
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The Correct Option is C
Solution and Explanation
The mutual of the system $M=\mu_{0} \,n_{1} \,n_{2} \,\pi\, a^{2}\, L$
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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