Tag: electromagnetic induction

Questions Related to electromagnetic induction

When the current in a coil changes from 8 ampere to 2 ampere in $3 \times 10^{-2}$ second, the e.m.f. induced in the coil is 2 volt. The self inductance of the coil (in millinery) is

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 1

  2. 5

  3. 20

  4. 10

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Correct Option: A
Explanation:

$E.M.F. = L \dfrac{di}{dt}$


$2 = L \times \dfrac{8-2}{3 \times 10^{-2}}$

L = 1 millinery

Here (A) is correct answer

Two coils have mutual inductance $0.005 H$. The current changes in the form coil according to equation, $ I = I _0 \sin \omega t . $ Where $ I _0 = 10 A. $ and $ \omega = 100 \pi $ rads/s. The maximum value of emf in the second coil is :

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $ 12 \pi $

  2. $ 8 \pi $

  3. $ 5 \pi $

  4. $ 2 \pi $

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Correct Option: C
Explanation:
Mutual inductance between two coils
M = 0.005 H 
Peak current $ l _0 = 10 A $
Angular frequency $ \omega = 100 \pi $ rad/s
Current $ l = l _0 \sin \omega t $
$ \dfrac {d}{dt} = \dfrac {d}{dt} ( l \sin \omega t ) $
$ = l _0 \cos \omega t . \omega $
$ = 10 \times 1 \times 100 \pi $
$ = 1000 \pi $
Hence, induced emf is given by 
$ E = M \times \dfrac {dl}{dt} $
$ = 0.005 \times 1000 \times \pi = 5 \pi V $

A coil of area 500 $cm^2$ having 1000 turns is placed such that the plane of the coil is perpendicular to a magnetic field of magnitude $4 \times 10^{-5}$ $weber/m^2$. If it is rotated by 180 about an axis passing through one of its diameter in 0.1 sec, find the average induced emf.

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. zero.

  2. 30 mV

  3. 40 mV

  4. 50 mV

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Correct Option: C
Explanation:
0iven that :-  $N=1000, B=4\times 10^{-5}weber/m^2, A=500cm^2=0.05m^2$

Initial flux linked with the coil, $\phi _1=1000\times 4\times 10^{-5}\times 0.05$

$\implies \phi _1=2\times 10^{-3}weber$

After rotation of $180^{o}$, B remains same but normal vector gets reversed, hence $\phi _2=-\phi _1$

Average EMF=$E=\dfrac{-\Delta \phi}{t}$

$\implies E=-\dfrac{\phi _2-\phi _1}{t}$

$\implies E=\dfrac{\phi _1-\phi _2}{t}$

$\implies E=\dfrac{2\phi _1}{t}$

$\implies E=\dfrac{4\times 10^{-3}}{0.1}V$

$\implies E=40mV$

Answer-(C)

A long straight wire is placed along the axis of a circular ring of radius $R$. The mutual inductance of this system is

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $\dfrac{\mu _{0}R}{2}$

  2. $\dfrac{\mu _{0}\pi R}{2}$

  3. $\dfrac{\mu _{0}}{2}$

  4. $0$

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Correct Option: D

A coil of $Cu$ wire (radius $-r$, self-inductance-$L$) is bent in two concentric turns each having radius $\dfrac{r}{2}$. The self-inductance is now

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $2L$

  2. $L$

  3. $4L$

  4. $\dfrac{L}{2}$

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Correct Option: C

Mutual inductance of a system of two thin coaxial conducting loops of radius 0.1 m, and then center separated by distance 10 m is (Take $\mu^{2} = 10$)

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $2 \times 10^{-20}$ H

  2. $2 \times 10^{-13}$ H

  3. $2 \times 10^{-18}$ H

  4. $2 \times 10^{-15}$ H

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Correct Option: A

A ring of radius $r$ is uniformly charged with charge $q.$ If the ring is rotated about it's axis with angular frequency $\omega$, then the magnetic induction at its centre will be-

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $10 ^ { - 7 } \times \frac { \omega } { q r }$

  2. $10 ^ { - 7 } \times \frac { 9 } { \omega r }$

  3. $10 ^ { - 7 } \times \frac { r } { q \omega }$

  4. $10 ^ { - 7 } \times \frac { q \omega } { r }$

Show answer
Correct Option: D
Explanation:

$\begin{array}{l} T=\dfrac { { 2\pi  } }{ w }  \ i=\dfrac { { qw } }{ { 2\pi  } }  \ B=\dfrac { { { \mu _{ 0 } }i } }{ { 2r } } =\dfrac { { { \mu _{ 0 } } } }{ { 2r } } \times \dfrac { { qw } }{ { 2\pi  } }  \ ={ 10^{ -7 } }\times \dfrac { { qw } }{ r }  \ Hence, \ option\, \, D\, \, is\, correct\, \, answer. \end{array}$

Give the MKS units for the following quantities.
Magnetic Induction.

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. Weber$/m^3$.

  2. Weber$/m^2$.

  3. Weber$/m^4$.

  4. Weber$/m^5$.

Show answer
Correct Option: B
Explanation:

B. $Weber/m^2$

The term magnetic flux density refers to the fact that B is magnetic flux per unit surface. This relationship is based on Faraday's law of magnetic induction.
The SI unit measuring the strength of B is T(Tesla= $Weber/m^2$)

Two coaxial coils are very close to each other and their mutual inductance is $5mH$. If a current $50\sin{500t}$ is passed on one of the coils then the peak value of induced emf in the secondary coil will be:

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $5000V$

  2. $500V$

  3. $150V$

  4. $125V$

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Correct Option: D
Explanation:

By the principle of mutual inductance we know that flux induced in coil2 will depend on the current flowing in coil1

$\phi _1=Mi _1$
Here
M=Mutual inductance
$i _1$=current in 1st coil 
Now by Faraday's law induced emf in 2nd coil will be 
$\frac { d\Phi  }{ dt }=emf$
$emf=M\frac{di _1}{dt}$
Now put value of current and mutual inductance
$emf=(5\times 10^{-3}) \frac{d (50\sin500t)}{dt} $
$emf=(5\times 10^{-3})\times 50\times 500\times \cos500t$
$emf=125\cos500t$
So above is the equation of induced emf
So maximum value of induced emf will be
$emf _{max}=125 volts$

A solenoid would over a rectangular frame. If all the linear dimensions of the frame are increased by a factor $3$ and the number of turns per unit length remains the same, the inductance increased by a factor of :-

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $3$

  2. $9$

  3. $27$

  4. $63$

Show answer
Correct Option: B
Explanation:

Firstly, the relation between inductance and length is calculated


$ emf=\dfrac{-Nd\phi }{dt}=-NA\dfrac{dB}{dt} $

$ B=\mu \dfrac{N}{l}I $

$ emf=-\dfrac{\mu {{N}^{2}}A}{l}\dfrac{dI}{dt} $

$ emf=-L\dfrac{dI}{dt} $

$ L=\dfrac{\mu {{N}^{2}}A}{l} $

So, L is inversely proportional to length of solenoid.

If all the linear dimensions of the frame are increased by a factor 3 and the number of turns per unit length remains the same

Then area $\begin{align}

$ A=3l\times 3b $

$ =9lb $

$ {{L}^{'}}=\dfrac{9{{\mu }_{0}}{{N}^{2}}A}{l} $

$ L'=9\,L $

So new inductance becomes 9 times.