Tag: electromagnetic induction

Questions Related to electromagnetic induction

What is inductance of a 25 cm long solenoid if it has 1000 turns an radius of its circular cross-section is 5 cm ?

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 0.04 H

  2. 0.02 H

  3. 0.8 H

  4. 0.1 H

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Correct Option: B

A coil of mean area 500 $cm^2$ and having 1000 turns is held perpendicular to a uniform field of 0.4 gauss. The coil is turned through $180^o$ in $\frac{1}{10}$second. The average induced e.m.f. :-

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $0.04 V$

  2. $0.4 V$

  3. $4 V$

  4. $0.004 V$

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Correct Option: A

The M.I. of a disc  about its diameter is $2$ units. Its M.I. about axis through a point on its rim in the plane of the disc is

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $4$ units

  2. $6$ units

  3. $8$ units

  4. $10$ units

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

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

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

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

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Correct Option: D
Explanation:

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

The self inductance of a coil having $500$ turns is $50$ mH. The magnetic flux through the cross-sectional area of the coil while current through it is $8$mA is found to be?

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $4\times 10^{-4} Wb$

  2. $0.04$ Wb

  3. $4\mu$ Wb

  4. $40$m Wb

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Correct Option: A
Explanation:
Given that,

Number of turns $N =500$

Self inductance $L=50\times10^{-3}\ H$

Current $I=8\times10^{-3}\ A$

The magnetic flux through an inductor is the self inductance of coil times the current through it.

The flux is 
$\phi=LI$

$\phi=50\times10^{-3}\times8\times10^{-3}$

$\phi=4\times10^{-4}\ Wb$

So, the magnetic flux is $4\times10^{-4}\ Wb$

Hence, A is correct option.

What is the mutual inductance of coil and solenoid if a solenoid of length $0.50\ m$ and with $5000$ turns of wire has a radius $4\ cm$ and a coil of $700$ turns is wound on the middle part of the solenoid?

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $44.17\ mH$

  2. $48.98\ mH$

  3. $34.34\ mH$

  4. $36.73\ mH$

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Correct Option: A

The mutual inductance of an induction coil is 5 H. In the primary coil, the current reduces from 5 A to zero in $10^{-3} s$. What is the induced e.m.f. in the secondary coil?

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 2500 V

  2. 25000 V

  3. 2510 V

  4. zero

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Correct Option: B
Explanation:

$EMF=L\dfrac { di }{ dt } $

$=5\times \dfrac { 5 }{ { 10 }^{ -3 } } $

$=25000V$

Two concentric rings are kept in the same plane. Number of turns in each rings is $25$. Their radii are $50 cm$ and $200 cm$ and they carry electric currents of $0.1 A$ and $0.2 A$ respectively, in mutually opposite directions. The magnitude of the magnetic field produced at their centre is ____________ $T$.

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

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

  2. $4{ \mu } _{ 0 }$

  3. $\dfrac { 10 }{ 4 } { \mu } _{ 0 }$

  4. $\dfrac { 5 }{ 4 } { \mu } _{ 0 }$

Show answer
Correct Option: D
Explanation:

Given, ${ N } _{ 1 }={ N } _{ 2 }=25$ turns
           ${ R } _{ 1 }=50 cm=0.5 m$
           ${ R } _{ 2 }=200 cm=2 m$
           ${ i } _{ 1 }=0.1A, { i } _{ 2 }=0.2A$
The magnitude of the magnetic field
$\Delta B={ B } _{ 1 }-{ B } _{ 2 }$
           $=\dfrac { { \mu  } _{ 0 }{ N } _{ 1 }{ i } _{ 1 } }{ 2{ R } _{ 1 } } -\dfrac { { \mu  } _{ 0 }{ N } _{ 2 }{ i } _{ 2 } }{ 2{ R } _{ 2 } } $
           $=\dfrac { { \mu  } _{ 0 }\times 25 }{ 2 } \left( \dfrac { { i } _{ 1 } }{ { R } _{ 1 } } -\dfrac { { i } _{ 2 } }{ { R } _{ 2 } }  \right) $
           $=\dfrac { { \mu  } _{ 0 }\times 25 }{ 2 } \left( \dfrac { 0.1 }{ 0.5 } -\dfrac { 0.2 }{ 2 }  \right) $
           $=\dfrac { 25 }{ 2 } { \mu  } _{ 0 }\left( \dfrac { 1 }{ 5 } -\dfrac { 1 }{ 10 }  \right) $
           $=\dfrac { 25 }{ 2 } { \mu  } _{ 0 }\left( \dfrac { 2-1 }{ 10 }  \right)$
           $=\dfrac { 25 }{ 2 } { \mu  } _{ 0 }\times \dfrac { 1 }{ 10 } =\dfrac { 25 }{ 20 } { \mu  } _{ 0 }=\dfrac { 5 }{ 4 } { \mu  } _{ 0 }$

A solenoid of length 30 cm with 10 turns per centimetre and area of cross-Section 40 $cm^2 $completely surrounds another co-axial solenoid of same length, area of Cross-section 20 $cm^2$ with 40 turns per centimetre. The mutual inductance of the

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 10 H

  2. 8 H

  3. 3mH

  4. 30 mH

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Correct Option: C
Explanation:

Given:

$n _1 = 10cm^{-1} = 1000 m^{-1}$
$n _2 = 40cm^{-1} = 4000 m^{-1}$
$l= 30cm = 30 \, \times \, 10m^{-2}$
$A _2 = 20cm^2 = 20 \, \times \, 10^{-4}m^2$

Mutual inductance of the system,
$M \, = \, \mu _0n _1n _2A _2l$                                  (Where $A _2$ is the area of inner solenoid.)


$\therefore M = 4\pi  \times  10^{-7} \times  1000 \times 4000 \times 20 \times 10^{-4} \times 30 \times  10^{-2}$
   $M= 301.44 \, \times 10^{-5} H = 3mH$

A 2 m long solenoid with diameter 2 cm an 2000 turns has a secondary coil of 1000 turns wound closely near its midpoint. The mutual inductance between the two coils is

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $2.4\times 10^{-4}$ H

  2. $3.9\times 10^{-4}$ H

  3. $1.28\times 10^{-3}$ H

  4. $3.14\times 10^{-3}$ H

Show answer
Correct Option: B
Explanation:

Here, $l = 2 m$, diameter = 2 cm
$\therefore \, radius, \, r = \dfrac{2}{2} = 1cm = 1 \, \times \,10^{-2}m$

$N _1$ = 2000, $N _2$ = 1000

Area = $\pi r^2$  =  $\pi \, \times \, \left ( 1\times 10^{-2} \right )^2 = 3.14 \times 10^{-4} m^2$

Mutual inductance, M = $\dfrac{\mu _0N _1N _2A}{l}$

$\,= \, \dfrac{4\pi \,\times \,10^{-7}\, \times \, 2000 \, \times \, 1000 \, \times \, 3.14 \,\times \,10^{-4}}{2}$
$M=3.9 \, \times \, 10^{-4}H$