Tag: electromagnetic induction

Questions Related to electromagnetic induction

A pair of adjacent coils has a mutual inductance of 2.5 H. If the current in one coil changes from 0 to 40 A in 0.8 s, then the change in flux linked with the other coil is then

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 100 Wb

  2. 120 Wb

  3. 200 Wb

  4. 250 Wb

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Correct Option: A
Explanation:

Mutual inductance of a pair of coils,, $M=2.5\ H$


Initial current, $i _1=0\ A$

Final current, $i _2=40\ A$

Change in current, $di=i _2-i _1=40\ A$

Time taken for the change, $t= 0.8\ sec$

Induced e.m.f, $e= \dfrac{d\phi}{dt}= M\dfrac{di}{dt}$

where $d\phi$ is the change in the flux linked with the coil.

$\implies d\phi = Mdi =2.5\times 40 =100\ Wb$

Hence, the change in the flux linkage is $100\ Wb$.

So,  option $(A) is correct. 

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, the number of turns per Unit length $n _2$. What is the mutual inductance of the system?

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $\mu _0\pi b^2 n _1 n _2 L $

  2. $\mu _0\pi a^2 n _1 n _2 L ^2$

  3. $\mu _0\pi a^2 n _1 n _2 L $

  4. $\mu _0\pi b^2 n _1 n _2 L ^2$

Show answer
Correct Option: C
Explanation:

Let $L$ be the length of each solenoid $S _1$ and $S _2$ having radius a and b respectively.

$n _1$ and $n _2$ be the number of turns per unit length of $S _1$ and $S _2$.
And $I$ be the current through solenoid $S _2$
Magnetic field in $S _2= B _2= {\mu _0n _2I}$
Magnetic flux linked with each turn of $S _1 = B _2 \times $ area of each turn $= B _1\pi a^2$

Total magnetic flux linked with $S _1= B _2\pi a^2n _1L$

$\therefore \phi _1 = \left({\mu _0n _2I}\right)\pi a\ ^2n _2L = {\mu _0n _1n _2 \pi a^2 I}{L}$

But magnetic flux linked with $S _1$ is due to $I$
$\therefore \phi _1 \propto I$    or     $\phi _1 = M\ I$

Where $M$ is the mutual inductance of $S _2$ and $S _1$
$\therefore M \, I = {\mu _0n _1n _2\pi a^2I}{L}$

$\therefore M = \mu _0n _1n _2\pi a^2L$

Two short bar magnets of magnetic moment 'M' each are arranged at the opposite corners of a square of side 'o', such that their centres coincide with the square. If the like poles are in the same direction, the magnetic induction at any of the other of the square is

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $\frac { { \mu } _{ 0 } }{ 4\pi } \frac { M }{ { d }^{ 3 } } $

  2. $\frac { { \mu } _{ 0 } }{ 4\pi } \frac { 2M }{ { d }^{ 3 } } $

  3. $\frac { { \mu } _{ 0 } }{ 2\pi } \frac { 3M }{ { d }^{ 3 } } $

  4. $\frac { { \mu } _{ 0 } }{ 2\pi } \frac { 2M }{ { d }^{ 3 } } $

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Correct Option: A

A conducting ring of radius r and resistance R rolls on a horizontal surface with constant velocity v. 

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. The induced emf.between O and Q is 2 Bvr.

  2. An induced current $ I= \dfrac { 2Bvr }{ R } $ flows in the clockwise direction.

  3. An induced current $ I= \dfrac { 2Bvr }{ R } $ flows in the anticlockwise direction.

  4. No current flows

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Correct Option: D

Two coils of self-inductances $2\ mH$ and $8\ mH$ are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $10\ mH$

  2. $6\ mH$

  3. $4\ mH$

  4. $16\ mH$

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Correct Option: C
Explanation:

Mutual inductance M=$\sqrt{ L _1\times L _2}=\sqrt{ 2\times 8}=4$mH

Mutual inductance of a system of two thin coaxial conducting loops of radius each, their centers separated by distance $d (d >>r)$ is 

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $\mu _0\pi r^4d^3$

  2. $\dfrac{\mu _0\pi r^4}{2d^3}$

  3. $\dfrac{\mu _0\pi r^4}{d^3}$

  4. $\dfrac{\mu _0\pi r^4 d^3}{4}$

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Correct Option: B

The coefficient of mutual inductance, when magnetic flux changes by $\displaystyle 2\times { 10 }^{ -2 }Wb$ and current changes by 0.01 A is :

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 8 henry

  2. 4 henry

  3. 3 henry

  4. 2 henry

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Correct Option: D
Explanation:

We know that

$\displaystyle \phi =Mi$
$\displaystyle d\phi =Mdi$

$\displaystyle M=\frac { d\phi  }{ di } =\frac { 2\times { 10 }^{ -2 } }{ 1\times { 10 }^{ -2 } } =2$ henry