Tag: electromagnetic induction

Questions Related to electromagnetic induction

The coefficient of self induction of two inductor coils are $20mH$ and $40mH$ respectively. If the coils are connected in series so as to support each other and the resultant inductance is $80mH$ then the value of mutual inductance between the coils will be

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $5mH$

  2. $10mH$

  3. $20mH$

  4. $40mH$

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Correct Option: B
Explanation:

$L _{total} = L _1 + L _2 + 2M$


$80 mH = 20 mH + 40 mH + 2M$

$\therefore M = 10 mH$

For solenoid keeping the turn density constant its length makes halved and its cross section radius is doubled then the inductance of the solenoid increased by :

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $200\%$

  2. $100\%$

  3. $800\%$

  4. $700\%$

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Correct Option: B

A rectangular loop of sides 'a' and 'b' is placed in the XY plane. A very long wire is also placed in xy plane such that side of length 'a' of the loop is parallel to the wire. The distance between the wire and the nearest edge of the loop is 'd'. The mutual inductance of this system is proportional to?

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. a

  2. b

  3. $1/d$

  4. Current in wire

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Correct Option: A

A circular loop of radius $r$ is placed at the centre of current carrying conducting square loop of side $a$. If both loops are coplanar and $a >> r$, then the mutual inductance between the loops will be:

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $\dfrac{\mu _0r^2}{2\sqrt{2}(a)}$

  2. $\dfrac{\mu _0r^2}{4a}$

  3. $\dfrac{2\sqrt{2}\mu _0r^2}{\pi a}$

  4. $\dfrac{\mu _0r^2}{4\sqrt{2}a}$

Show answer
Correct Option: C
Explanation:

Both loops are coplanar. 

Magnetic field at the center of outer square current carrying loop is
${ B } _{ 1 }=\dfrac { 2\sqrt { 2 } { \mu  } _{ 0 }I }{ \pi a } $
where $a$= length of side of square loop and
$r$= radius of the circular loop.
Given $a>>r$,
The magnetic field through entire inner coil is ${ B } _{ 1 }$
Magnetic flux through inner coil, ${ \phi  } _{ 21 }={ B } _{ 1 }{ A } _{ 2 }$
        =$\dfrac { 2\sqrt { 2 } { \mu  } _{ 0 }I }{ \pi  } \dfrac { { r }^{ 2 } }{ a } $------ (1)
    Mutual induction, M= $\dfrac { \phi  }{ { I } _{ 1 } } $

From (1), M= $\dfrac { 2\sqrt { 2 } { \mu  } _{ 0 } }{ \pi  } \dfrac { { r }^{ 2 } }{ a } $

Hence, $M\alpha \dfrac { { r }^{ 2 } }{ a } $

A $50\ Hz$ $AC$ current of crest value $1\ A$ flows, through the primary of transformer. If the mutual inductance between the primary and secondary be $0.5\ H$, the crest voltage induced  in the secondary is

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 75 V

  2. 150 V

  3. 100 V

  4. 300V

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Correct Option: D

Which of the following statement is correct?

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. when the magnetic flux linked with conducting loop is zero then emf induced is always zero

  2. when the emf induced in conducting loop is zero, then the magnetic flux linked with the loop must be zero

  3. transformer works on mutual induction

  4. all of these

Show answer
Correct Option: A,C
Explanation:

 Statement is.

A) When the magnetic flux linked with conducting loop is zero then emf induced is always zero.
     $emf=\dfrac{d\phi}{dt}$
  If $\phi=0$, $emf=\dfrac{d0}{dt}=0$
B) when the emf induced in conducting loop is zero, then the magnetic flux linked with the loop must be zero.
    $emf=\dfrac{d\phi}{dt}=0$
    $d\phi=0$
   $\phi=constant$ magnetic flux is constant.
This is the wrong statement
C) The transformer works on mutual induction.
The correct statement is (A) and (C).


An electron originates at a point $A$ lying on the axis of a straight solenoid and moves with velocity $v$ at an angle $\alpha$ to the axis. The magnetic induction of the field is equal to $BA$ screen is oriented at right angles to the axis and is located at a distance $1$ from the point $a$. Find the distance from the axis to the point on the screen into which the electron strikes.

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $d = 5r\sin \left (\dfrac {\theta}{2}\right )$, Here $r = 2\dfrac {mv\sin \alpha}{eB}$ and $\theta = \dfrac {eBl}{mv\cos \alpha}$.

  2. $d = 2r\sin \left (\dfrac {\theta}{2}\right )$, Here $r = \dfrac {mv\sin \alpha}{eB}$ and $\theta = \dfrac {eBl}{mv\cos \alpha}$.

  3. $d = 3r\sin \left (\dfrac {\theta}{2}\right )$, Here $r = 3\dfrac {mv\sin \alpha}{eB}$ and $\theta = \dfrac {eBl}{mv\cos \alpha}$.

  4. $d = 4r\sin \left (\dfrac {\theta}{2}\right )$, Here $r = \dfrac {mv\sin \alpha}{eB}$ and $\theta = \dfrac {eBl}{mv\cos \alpha}$.

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Correct Option: B

When current breaks in primary coil current reaches to zero in  second. Emf induced in the secondary coil is 20,000V and mutual inductance between the coils is 5H. The maximum current is the primary before the break is

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 0.2 amp

  2. 0.4 amp

  3. 4 amp

  4. 2 amp

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Correct Option: B

Two conducting circular loops of radii $R _{1}$ and $R _{2}$ are placed in the same plane with their centres coinciding. If $R _{1} \gg R _{2}$, the mutual inductance $M$ between them will be directly proportional to

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $R _{1}/R _{2}$

  2. $R _{2}/R _{1}$

  3. $R _{1}^{2}/R _{2}$

  4. $R _{2}^{2}/R _{1}$

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Correct Option: D

The mutual inductance $M _{12}$ of coil 1 with respect to coil 2

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. increases when they are bought nearer.

  2. depends on the current passing through the coils.

  3. increases when one of them is rotated about an axis.

  4. is not same as $M _{21}$ of coil 2 with respect to coil 1.

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Correct Option: A