Tag: electromagnetic induction

Questions Related to electromagnetic induction

A long solenoid  of diameter $0.1\ m$ has $2 \times {10^4}$ turns per metre.At the centre of the solenoid, a coil of $100$ turns and radius $0.01\ m$ is placed with its axis coinciding with the solenoid axis.The current in the solenoid reduces at a constant rate to $0\ A$ from $4\ A$ in $0.05\ s$. If the resistance of the coil is $10 \ {\pi ^2}\Omega ,$ the total charge flowing through the coil during this time is.

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $32\ \pi \mu C$

  2. $16\ \mu C$

  3. $32\ \mu C$

  4. $16\ \pi \mu C$

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Correct Option: C
Explanation:
Given,

Number of turns, $n=100$

Radius, $r=0.01\,m$

Resistance, $R=10\pi^2 \Omega$

As we know,

$\epsilon=-N\dfrac{d\phi}{dt}$

$=\dfrac{\epsilon}{R}=-\dfrac NR\dfrac{d\phi}{dt}$,   $\Delta I=-\dfrac NR\dfrac{d\phi}{dt}$

$\dfrac{\Delta}{\Delta t}=-\dfrac NR\dfrac{\Delta\phi}{\Delta t}\implies \Delta q=-[\dfrac NR(\dfrac{\Delta \phi}{\Delta t})]\Delta t$

$-$ve sign shoes that induced emf opposes the change in flux.

$\Delta q=\dfrac{\mu _0 ni\pi r^2}{R}$

$\Delta q=\dfrac{4\pi\times 10^{-7}\times 100\times 4\times \pi\times (0.01)^2}{10\pi^2}=32\mu C$

Two coils, a primary of $400$ turns and a secondary of $20$ turns are wound over an iron core of length $20\pi\ cm$ and cross-section of $2\ cm$ radius. If $\mu _{r}=800$, then the coefficient of mutual induction is approximately

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $1.6\times 10^{7}H$

  2. $1.6\times 10^{-2}H$

  3. $1.6\times 10^{3}H$

  4. $1.6\ H$

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Correct Option: A

A charge of ${10^{ - 6}}C$ is describing a circular path of radius $1$ cm making $5$ revolution per second . The magnetic induction field at the centre of the circle is 

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $\pi \times {10^{ - 10}}T$

  2. $\pi \times {10^{ - 9}}T$

  3. $\frac{\pi }{2} \times {10^{ - 10}}T$

  4. $\frac{\pi }{2} \times {10^{ - 9}}T$

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Correct Option: D

Two coils A and B have mutual inductance $2\times { 10 }^{ -2 }$ henry. If the current in the primary is $i=5\sin { \left( 10\pi t \right)  } $ then the maximum value of e.m.f.induced in coil B is 

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $\pi \quad volt$

  2. $\pi /2volt$

  3. $\pi /3volt$

  4. $\pi /4volt$

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Correct Option: A

When the primary current in the spark-coil of a car changes from $4A$ to zero in $10\mu s$, an emf of $40000$V is induced in the secondary. The mutual inductance between the primary and the secondary winding of the spark-coil will be-

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 1 H

  2. 0.1 H

  3. 10 H

  4. zero

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Correct Option: A

Two coils A and B have mutual inductance $2\times { 10 }^{ -2 }$ henry. If the current in the primary is $i=5\sin { \left( 10\pi t \right)  } $ then the maximum value of e.m.f. induced in coil B is

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $\pi \quad volt$

  2. $\pi /2volt$

  3. $\pi /3volt$

  4. $\pi /4volt$

Show answer
Correct Option: A

The electric field of an electromagnetic wave is given by, $E=(50N^{-1})\, \sin { \omega  } (t-x/c)$. Find the energy contained in a cylinder of cross section $10cm^2$ and length $50 cm$ along the x-axis.

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $5.5\times 10^{-12}J$

  2. $4.5\times 10^{-12}J$

  3. $5\times 10^{-13}J$

  4. $3.5\times 10^{-10}J$

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Correct Option: A

An electron having kinetic energy T is moving in a circular orbit of radius R perpendicular to a uniform magnetic induction $\vec { \mathrm { B } }$  If kinetic energy is doubled and magnetic induction tripled, the radius will

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $\frac { 3 R } { 2 }$

  2. $ \frac{{\sqrt 2 }}{3}R$

  3. $\sqrt { \frac { 2 } { 9 } } R$

  4. $\sqrt { \frac { 4 } { 3 } } R$

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Correct Option: B
Explanation:

We know$,$

$R = \frac{{\sqrt {2mk} }}{{qB}}$
$R' = \frac{{\sqrt {2m2k} }}{{q\left( {3B} \right)}}$
$ = \frac{{\sqrt 2 }}{3}\frac{{\sqrt {2mk} }}{{qB}}$
$ = \frac{{\sqrt 2 }}{3}R$
Hence,
option $(B)$ is correct answer.

An average induced emf of 0.4 V appears in a coil when the current in it is changed from 10 A in one direction to 10 A in opposite direction in 0.5 sec. self-inductance of the coil is.

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 0.008H

  2. 50 H

  3. 75 H

  4. 100 H

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Correct Option: A

At any instant t currenetI thorugh a coil of sself inductance 2mH is given.The induced e.m.f will be zero at time    

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 1 sec

  2. 2 sec

  3. 3 sec

  4. 4 sec

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Correct Option: B