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Electromagnetic Induction — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsElectromagnetic Induction4 Marks
Question
(a) Define mutual inductance and write its S.I. unit.
(b) A square loop of side 'a' carrying a current $I_{2}$ is kept at distance x from an infinitely long straight wire carrying a current $I_{1}$ as shown in the figure. Obtain the expression for the resultant force acting on the loop.
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Answer

(a) Mutual Induction : "It is the phenomenon of electromagnetic induction in which induced emf is produced in the another coil placed near by a coil in which magnetic flux is changed by changing the current in this coil."
SI. Unit of Mutual Induction is Henry (H).
(b) TThe resultant magnetic force of sides AB and DC is zero. The force on side AD is repulsive and on side BC is attractive. Since, AD is neal the straight wire. So the net force will be repulsive.
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Force on side AD,
$F_{1}=\frac{\mu_{0}I_{1}I_{2}a}{2\pi x}$ (away from wire)
Force on side BC,
$F _2=\frac{\mu_0 I _1 I _2 a}{2 \pi(x+a)} \times a$ (toward the wire)
Thus,
$F=F_{1}-F_{2}$
$=\frac{\mu_{0}}{2\pi}I_{1}I_{2}a(\frac{1}{x}-\frac{1}{x+a})$
$F=\frac{\mu_{0}}{2\pi}I_{1}I_{2}a(\frac{a}{x(x+a)})$
$F=\frac{\mu_{0}}{2\pi} \times \frac{I_{1}I_{2}a^{2}}{x(x+a)}$

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