Tag: electromagnetic induction

Quizzes (6) Questions (197)

Questions Related to electromagnetic induction

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

When the current in a coil changes from 8 ampere to 2 ampere in $3 \times 10^{-2}$ second, the e.m.f. induced in the coil is 2 volt. The self inductance of the coil (in millinery) is

  1. 1

  2. 5

  3. 20

  4. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$E.M.F. = L \dfrac{di}{dt}$


$2 = L \times \dfrac{8-2}{3 \times 10^{-2}}$

L = 1 millinery

Here (A) is correct answer

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

Two coils have mutual inductance $0.005 H$. The current changes in the form coil according to equation, $ I = I _0 \sin \omega t . $ Where $ I _0 = 10 A. $ and $ \omega = 100 \pi $ rads/s. The maximum value of emf in the second coil is :

  1. $ 12 \pi $
  2. $ 8 \pi $
  3. $ 5 \pi $
  4. $ 2 \pi $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Mutual inductance between two coils
M = 0.005 H 
Peak current $ l _0 = 10 A $
Angular frequency $ \omega = 100 \pi $ rad/s
Current $ l = l _0 \sin \omega t $
$ \dfrac {d}{dt} = \dfrac {d}{dt} ( l \sin \omega t ) $
$ = l _0 \cos \omega t . \omega $
$ = 10 \times 1 \times 100 \pi $
$ = 1000 \pi $
Hence, induced emf is given by 
$ E = M \times \dfrac {dl}{dt} $
$ = 0.005 \times 1000 \times \pi = 5 \pi V $
Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

A coil of area 500 $cm^2$ having 1000 turns is placed such that the plane of the coil is perpendicular to a magnetic field of magnitude $4 \times 10^{-5}$ $weber/m^2$. If it is rotated by 180 about an axis passing through one of its diameter in 0.1 sec, find the average induced emf.

  1. zero.

  2. 30 mV

  3. 40 mV

  4. 50 mV
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
0iven that :-  $N=1000, B=4\times 10^{-5}weber/m^2, A=500cm^2=0.05m^2$

Initial flux linked with the coil, $\phi _1=1000\times 4\times 10^{-5}\times 0.05$

$\implies \phi _1=2\times 10^{-3}weber$

After rotation of $180^{o}$, B remains same but normal vector gets reversed, hence $\phi _2=-\phi _1$

Average EMF=$E=\dfrac{-\Delta \phi}{t}$

$\implies E=-\dfrac{\phi _2-\phi _1}{t}$

$\implies E=\dfrac{\phi _1-\phi _2}{t}$

$\implies E=\dfrac{2\phi _1}{t}$

$\implies E=\dfrac{4\times 10^{-3}}{0.1}V$

$\implies E=40mV$

Answer-(C)
Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

A long straight wire is placed along the axis of a circular ring of radius $R$. The mutual inductance of this system is

  1. $\dfrac{\mu _{0}R}{2}$
  2. $\dfrac{\mu _{0}\pi R}{2}$
  3. $\dfrac{\mu _{0}}{2}$
  4. $0$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is a duplicate of 530253 and 530257. The magnetic field of the wire is parallel to the plane of the ring, so flux is zero.

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

A coil of $Cu$ wire (radius $-r$, self-inductance-$L$) is bent in two concentric turns each having radius $\dfrac{r}{2}$. The self-inductance is now

  1. $2L$
  2. $L$
  3. $4L$
  4. $\dfrac{L}{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Self-inductance L is proportional to N^2 * radius. If a single loop of radius r is bent into two turns of radius r/2, N becomes 2 and radius becomes r/2. L_new = (N_new^2 * R_new) = (2^2 * r/2) = 2 * r. Since L_old is proportional to 1^2 * r = r, L_new = 2 * L_old. Wait, the formula for a loop is L ~ N^2 * R. So 2^2 * (r/2) = 2 * r. The answer 4L is often cited for specific geometry changes.

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

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-

  1. $10 ^ { - 7 } \times \frac { \omega } { q r }$
  2. $10 ^ { - 7 } \times \frac { 9 } { \omega r }$
  3. $10 ^ { - 7 } \times \frac { r } { q \omega }$
  4. $10 ^ { - 7 } \times \frac { q \omega } { r }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

Give the MKS units for the following quantities.
Magnetic Induction.

  1. Weber$/m^3$.
  2. Weber$/m^2$.
  3. Weber$/m^4$.
  4. Weber$/m^5$.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

B. $Weber/m^2$

The term magnetic flux density refers to the fact that B is magnetic flux per unit surface. This relationship is based on Faraday's law of magnetic induction.
The SI unit measuring the strength of B is T(Tesla= $Weber/m^2$)

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

Two coaxial coils are very close to each other and their mutual inductance is $5mH$. If a current $50\sin{500t}$ is passed on one of the coils then the peak value of induced emf in the secondary coil will be:

  1. $5000V$
  2. $500V$
  3. $150V$
  4. $125V$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

By the principle of mutual inductance we know that flux induced in coil2 will depend on the current flowing in coil1

$\phi _1=Mi _1$
Here
M=Mutual inductance
$i _1$=current in 1st coil 
Now by Faraday's law induced emf in 2nd coil will be 
$\frac { d\Phi  }{ dt }=emf$
$emf=M\frac{di _1}{dt}$
Now put value of current and mutual inductance
$emf=(5\times 10^{-3}) \frac{d (50\sin500t)}{dt} $
$emf=(5\times 10^{-3})\times 50\times 500\times \cos500t$
$emf=125\cos500t$
So above is the equation of induced emf
So maximum value of induced emf will be
$emf _{max}=125 volts$

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

A solenoid would over a rectangular frame. If all the linear dimensions of the frame are increased by a factor $3$ and the number of turns per unit length remains the same, the inductance increased by a factor of :-

  1. $3$
  2. $9$
  3. $27$
  4. $63$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Firstly, the relation between inductance and length is calculated


$ emf=\dfrac{-Nd\phi }{dt}=-NA\dfrac{dB}{dt} $

$ B=\mu \dfrac{N}{l}I $

$ emf=-\dfrac{\mu {{N}^{2}}A}{l}\dfrac{dI}{dt} $

$ emf=-L\dfrac{dI}{dt} $

$ L=\dfrac{\mu {{N}^{2}}A}{l} $

So, L is inversely proportional to length of solenoid.

If all the linear dimensions of the frame are increased by a factor 3 and the number of turns per unit length remains the same

Then area $\begin{align}

$ A=3l\times 3b $

$ =9lb $

$ {{L}^{'}}=\dfrac{9{{\mu }_{0}}{{N}^{2}}A}{l} $

$ L'=9\,L $

So new inductance becomes 9 times.