Tag: physics

Questions Related to physics

Two concentric coils each of radius equal to $2\pi\ cm$ are placed at right angles to each other. $3$ Ampere and $4$ ampere are the currents flowing in each coil respectively. The magnetic induction in $Weber/m^{2}$ at the centre of the coils will be ($\mu _{0}=4\pi \times 10^{-7}\ Wb/A-m$)

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $12\times 10^{-5}$

  2. $10^{-5}$

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

  4. $7\times 10^{-5}$

Show answer
Correct Option: C
Explanation:
Magnetic Induction at centre of coil is
$B=\dfrac {\mu _0}{2r} \sqrt {I _1^2 +I _2^2}\quad I _1=3\ A$
$I _2=4\ A$
$=\dfrac {4\pi\times 10^{-7}}{2\times \dfrac {2\pi}{100}}\times \sqrt {3^2 +4^2}$
$=\dfrac {4\pi \times 10^{-5}\times 5}{2\times 2\pi}$
$=5\times 10^{-5} \dfrac {wb}{m^2}$

A 60 volt - 10 watt bulb is operated at 100 volt - 60 Hz a.c. The inductance required is?

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 2.56 H

  2. 0.32 H

  3. 0.64 H

  4. 1.28 H

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Correct Option: D

Two coaxial coils are very close to each other and their mutual inductance is $5mH$. If a current $50sin{500t}$ is passed in 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. $125V$

Show answer
Correct Option: D
Explanation:

According to principle of mutual inductance, flux induced in coil  is equa to the current flowing in coil 1

$\phi _{2}= Mi _{1}$
By Faraday's laws,
$\dfrac{d\phi _{2}}{dt}=M\dfrac{di _{1}}{dt}$ = EMF
$\therefore EMF = 5\times 10^{-3}\dfrac{d}{dt}50 sin 500t$
$\therefore EMF = 125 cos500t$
So, maximum vaue of EMF would be 125 V

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. $40mH$

Show answer
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 $\theta = \dfrac {eBl}{mv\cos \alpha}$.

Show answer
Correct Option: B