Tag: magnetic fields and electromagnetism

Questions Related to magnetic fields and electromagnetism

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

The sun delivers ${10^3}W/{m^2}$ of electromagnetic flux to the earth's surface. The solar energy incident on the roof in $1$houre will be 

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

  1. $5.76 \times {10^8}J$

  2. $5.76 \times {10^7}J$

  3. $5.76 \times {10^6}J$

  4. $5.76 \times {10^5}J$

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Correct Option: C

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

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

  1. $1.2 \times 10 ^ { - 6 } N$

  2. $2 .4\times 10 ^ { - 6 } N$

  3. $2.16 \times 10 ^ { - 3 } \mathrm { N }$

  4. $1.5\times 10 ^ { - 6 } N$

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Correct Option: A
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.

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 ${ Nm }^{ 2 }/C?$

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

  1. $4.5\times { 10 }^{ 3 }$

  2. $3.5\times { 10 }^{ 3 }$

  3. $2.5\times { 10 }^{ 3 }$

  4. $1.5\times { 10 }^{ 3 }$

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Correct Option: A

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

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

  1. inversely with $I$

  2. inversely with ${ I }^{ 2 }$

  3. directly with $I$

  4. directly with ${ I }^{ 2 }$

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Correct Option: C