Tag: magnetic fields and electromagnetism

Quizzes (4) Questions (46)

Questions Related to magnetic fields and electromagnetism

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.

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

Light with an energy flux of $18 w/cm^2$ falls on a non-reflecting surface at normal incidence. If the surface has an area of $20 cm^2$. Find the average force exerted on the surface during a 30 minute time

  1. $1.2 \times 10 ^ { - 6 } N$
  2. $2 .4\times 10 ^ { - 6 } N$
  3. $2.16 \times 10 ^ { - 3 } \mathrm { N }$
  4. $1.5\times 10 ^ { - 6 } N$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total energy falling on the surface is $U = \left( {18W/c{m^2}} \right) \times \left( {20c{m^2}} \right) \times \left( {30 \times 60} \right) = 6.48 \times {10^5}J$

therefore$,$ the total momentum delivered is 
$P = \dfrac{U}{c} = \dfrac{{\left( {6.48 \times {{10}^5}J} \right)}}{{\left( {3 \times {{10}^8}\,m/s} \right)}} = 2.16 \times {10^{ - 3}}\,kgm/s$
The average force exerted on the surface is 
$F = \dfrac{p}{t} =  = \dfrac{{2.16 \times {{10}^{ - 3}}}}{{0.18 \times {{10}^4}}} = 1.2 \times {10^{ - 6}}N$
Hence,
option $(A)$ is correct answer.

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

The electric field in a certain region is $\left( 10\hat { i } +5\hat { j }  \right) \times { 10 }^{ 4 }N/C$. What is the flux due to this field over an area of $\left( 3\hat { i } +3\hat { j }  \right) \times { 10 }^{ -2 }{ m }^{ 2 }$ in ${ Nm }^{ 2 }/C?$

  1. $4.5\times { 10 }^{ 3 }$
  2. $3.5\times { 10 }^{ 3 }$
  3. $2.5\times { 10 }^{ 3 }$
  4. $1.5\times { 10 }^{ 3 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Electric flux is the dot product of the electric field vector and the area vector. Phi = (10i + 5j) * 10^4 * (3i + 3j) * 10^-2 = (30 + 15) * 10^2 = 45 * 10^2 = 4.5 * 10^3 Nm^2/C.

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

Current flowing through a long solenoid is varied. Then, magnetic flux density of the magnetic field inside varies ::

  1. inversely with $I$
  2. inversely with ${ I }^{ 2 }$
  3. directly with $I$
  4. directly with ${ I }^{ 2 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The magnetic field inside a long solenoid is given by B = mu0 * n * I, where n is the number of turns per unit length. Thus, B is directly proportional to the current I.