Tag: electromagnetic induction

Questions Related to electromagnetic induction

A sphere of radius $R$ and charge $Q$ is placed inside an imaginary sphere of radius $2R$. Whose center coincides with the given sphere. The flux related to the imaginary sphere is:

physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

  1. $\dfrac {Q}{\in _{0}}$

  2. $\dfrac {Q}{2\in _{0}}$

  3. $\dfrac {4Q}{\in _{0}}$

  4. $\dfrac {2Q}{\in _{0}}$

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Correct Option: A

The flux linked with a coil changes with time according to the equation $\phi$ = a$t^2$ +bt +c. Then SI unit of a is 

physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

  1. Volt

  2. Volt/sec

  3. Volt.sec

  4. Weber

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Correct Option: B
Explanation:

The unit of $\phi$ is Volt-sec.

Now $\phi=a t^{2}+bt+c$
To meet the dimension requirement $at^{2}$ must be Volt-sec.
$a$ must Volt/sec.

In a circuit a coil of resistance $2\,\Omega$, then magnetic flux charges from $2.0\,Wb$ to $10.0\,Wb$ in $0.2\ sec.$ The charge flow in the coil during this time is:

physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

  1. $5.0\ C$

  2. $4.0\ C$

  3. $1.0\ C$

  4. $0.8\ C$

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Correct Option: B
Explanation:

The relation between the rate of change of charge (or current) and the flux is given by the following relation:  

$ \because \dfrac{dQ}{dt}=-\dfrac{1}{R}\dfrac{d\phi }{dt} $

$ \dfrac{dQ}{dt}=\dfrac{-(10-2)}{2}=4\,C $


Two coils $A$ and $B$ are wound on the same iron  core as shown in figure. The number of turns in the coil $A$ and $B$ are $N _{A}$ and $N _{B}$ respectively. Identity the correct statement 

physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

  1. Both the coils have same magnitude of magnetic flux

  2. The magnetic flux linked are in the ratio $\dfrac{\phi A}{\phi B}=\dfrac{N _{A}}{N _{B}}$

  3. The induced emf across each coil are in the ratio $\dfrac{E _{A}}{E _{B}}=\left(\dfrac{N _{4}}{N _{B}}\right)^{2}$

  4. Both the coils have same magnitude of induced emf

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Correct Option: B

The magnetic flux through a stationary loop with resistance R varies during the interval of time T as $\phi  = at(T - t)$ ./ The heat generated during this time neglecting the inductance of the loop will be :

physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

  1. $\dfrac{{{a^2}{T^3}}}{{3R}}$

  2. $\dfrac{{{a^2}{T^2}}}{{3R}}$

  3. $\dfrac{{{a^2}T}}{{3R}}$

  4. $\dfrac{{{a^3}{T^3}}}{{3R}}$

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Correct Option: C

A circular disc of radius $0.2$m isplaced in a uniform magnetic field of induction $\dfrac{1}{\pi}\left(\dfrac {Wb}{m^2}\right)$ in such a way that its axis ,makes an angle of $60^o$ with $\xrightarrow {B}$. The magnetic flux linked with the disc is

physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

  1. $0.01$ Wb

  2. $0.02$ Wb

  3. $0.06$ Wb

  4. $0.08$ Wb

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Correct Option: A

The magnetic flux through a coil is $4\times 10^{-4} W/b/m^2$ at time $t=0$.It reduces to $10\%$ of its original value in 't' seconds.If the induced e.m.f is $0.72 m V,$ then the time t is:

physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

  1. $0.25 s$

  2. $0.05 s$

  3. $0.75 s$

  4. $1 s$

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Correct Option: B
Explanation:

As given in question

magnetic turn $=(\phi _1) = 4 \times 10^{-4}wb/m^2$
at $t = 0$
At, $t =t _2$, the turn reduces to $10\%$, means 
$\phi _2 = 0.9\ \phi _1$
As, per the farady's law,
In duced Emf $= \dfrac{Nd\ \phi}{dt}$
$e = \dfrac{nd\phi}{dt}$      ...(1)
$e = 0.72mu$ pur in (1), take $N = 1$ turns are constant
$0.72 \times 10^{-3} = \dfrac{-(\phi _2-\phi _1)}{(t _2-t _1)}$
$0.72\times 10^{-3} = \dfrac{-(0.9-2)\phi _1}{(t _2-0)}$
$t _2 = \dfrac{(0.1)\times (4\times 10^{-4})}{(0.72\times 10^{-3})}$
$t _2 = 0.05\ sec$

In a uniform electric field $\vec {E}$ an imaginary cube of edge length $a$ is considered as shown. The outward flux linked with cube surface will be :

physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

  1. $Ea^{2}$

  2. $\sqrt{2}Ea^{2}$

  3. $\sqrt{3}Ea^{2}$

  4. $2Ea^{2}$

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Correct Option: A

State whether the following two statements are true or false
(i) Li has the same units as that of magnetic flux.
(ii) Li has the units volt-second and magnetic flux has the units coulomb-ohm.

physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

  1. T T

  2. F F

  3. T F

  4. F T

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Correct Option: C
Explanation:

$\begin{array}{l} \left( 1 \right) This\, \, is\, \, True\, \, because\, \, \phi =Li \ \left( 2 \right) This\, \, is\, \, False\, \, because \ v=L\left( { \dfrac { { di } }{ { dt } }  } \right)  \ \Rightarrow L=\dfrac { v }{ q }  \ \Rightarrow Li=\dfrac { v }{ B }  \ Hence, \ option\, \, C\, \, is\, correct\, \, answer. \end{array}$

The ratio of magnetic inductions at the centre of a circular coil of radius a and on its axis at a distance equal to its radius, will be -

physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

  1. $\frac { 1 }{ \sqrt { 2 } } $

  2. $\frac { \sqrt { 2 } }{ 1 } $

  3. $\frac { 1 }{ 2\sqrt { 2 } } $

  4. $\frac { 2\sqrt { 2 } }{ 1 } $

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Correct Option: C