Tag: electromagnetic induction

Quizzes (6) Questions (197)

Questions Related to electromagnetic induction

Multiple choice physics magnetic fields and electromagnetism magnetic flux density magnetic flux 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:

  1. $\dfrac {Q}{\in _{0}}$
  2. $\dfrac {Q}{2\in _{0}}$
  3. $\dfrac {4Q}{\in _{0}}$
  4. $\dfrac {2Q}{\in _{0}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to Gauss's Law, the total electric flux through any closed surface is equal to the enclosed charge divided by epsilon_0. Since the inner sphere with charge Q is entirely enclosed by the imaginary sphere, the flux is Q/epsilon_0.

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

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:

  1. $5.0\ C$
  2. $4.0\ C$
  3. $1.0\ C$
  4. $0.8\ C$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $


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

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 

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

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 :

  1. $\dfrac{{{a^2}{T^3}}}{{3R}}$
  2. $\dfrac{{{a^2}{T^2}}}{{3R}}$
  3. $\dfrac{{{a^2}T}}{{3R}}$
  4. $\dfrac{{{a^3}{T^3}}}{{3R}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The induced emf is given by Faraday's law as e = -d(phi)/dt. Integrating the square of the current over time yields the total heat generated, H = integral((e^2)/R) dt. Evaluating this integral from t = 0 to t = T for phi = at(T - t) results in a^2 T^3 / (3R).

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

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:

  1. $0.25 s$
  2. $0.05 s$
  3. $0.75 s$
  4. $1 s$
Reveal answer Fill a bubble to check yourself
B Correct answer
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
$0.72 \times 10^{-3} = \dfrac{-(\phi _2-\phi _1)}{(t _2-t _1)}$
$0.72\times 10^{-3} = \dfrac{-(0.9-2)\phi _1}{(t _2-0)}$
$t _2 = \dfrac{(0.1)\times (4\times 10^{-4})}{(0.72\times 10^{-3})}$
$t _2 = 0.05\ sec$

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

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.

  1. T T

  2. F F

  3. T F

  4. F T
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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 -

  1. $\frac { 1 }{ \sqrt { 2 } } $
  2. $\frac { \sqrt { 2 } }{ 1 } $
  3. $\frac { 1 }{ 2\sqrt { 2 } } $
  4. $\frac { 2\sqrt { 2 } }{ 1 } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The magnetic induction at the center of a circular coil of radius a carrying current I is B_c = mu_0 I / (2a). The magnetic induction on its axis at a distance x = a is B_a = mu_0 I a^2 / (2(a^2 + a^2)^(3/2)) = mu_0 I / (4 sqrt(2) a). Taking the ratio B_c / B_a gives 2 sqrt(2) / 1.