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Electromagnetic Induction — Physics STD 12 Science — Question

Rajasthan 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 $2.0 \ cm^2$ 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?
✓

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, $\epsilon=\frac{d\phi_B}{dt}$
$=A\frac{dB}{Dt}$
$=\mu_0nA\frac{dI}{dt}$
$=4\pi\times10^{-7}\times1500\times2\times10^{-4}\times\frac{(4-2)}{0.1}\text{V}$
$=7.5\times10^{-6}\text{V}$

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