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Electromagnetic Induction — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsElectromagnetic Induction3 Marks
Question
  1. Define self-inductance. Write its SI units.
  2. A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?
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Answer

  1. Self-inductance is the amount of magnetic flux linked with a coil when a unit current flows through it.

(Alternatively, It is the amount of emf induced in a coil when current through it changes at the rate of 1 A per second.)

S.I. Unit: henry (H)

  1. Magnetic field inside the solenoid, $B=\mu_0\text{n I}$

Induced emf in the loop, $\in=\frac{d\phi_B}{dt}$

$=A\frac{dB}{Dt}$

$=\mu_0nA\frac{dI}{dt}$

$=4\pi\times10^{-7}\times1500\times2\times10^{-4}\times\frac{(4-2)}{0.1}\text{V}$

$=7.5\times10^{-6}\text{V}$

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