Tag: mutual inductance

Questions Related to mutual inductance

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

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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

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. $16\ \pi \mu C$

Show answer
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