Tag: electromagnetic induction

Questions Related to electromagnetic induction

Current $i _0$ is being carried by an infinite wire passing through origin along the direction $\hat{i} + \hat{j} + \hat{k}$. Find magnetic field due to the wire at point $(1 m, 0, 0)$.

  1. $\dfrac{(\mu _0 i)}{(2 \pi)} T$

  2. $\dfrac{(\mu _0 i)}{(\sqrt{2} \pi)} T$

  3. $\dfrac{(\mu _0 i)}{(4 \pi)} T$

  4. $\dfrac{(\sqrt{3} \mu _0 i)}{(2 \sqrt{2} \pi)} T$


Correct Option: D

A charge q is placed at the centre of a cylinder of radius R and length 2R. Then electric flux through the curved surface of the cylinder is 

  1. $\cfrac { q }{ 2 { \epsilon } _{ 0 } } $

  2. $\cfrac { q }{ 4 { \epsilon } _{ 0 } } $

  3. $\cfrac { q }{ \sqrt { 2 } { \epsilon } _{ 0 } } $

  4. $\cfrac { q }{ 2\sqrt { 2 } { \epsilon } _{ 0 } } $


Correct Option: C

A Point source generates 10 J of light energy in 2 s. The luminous flux of source is: 

  1. 5 lumen

  2. 10 lumen

  3. 50 lumen

  4. none of these


Correct Option: A
Explanation:

The luminous flux of source is the rate at which light energy flows from the source:

luminous flux =10 J/ 2 s= 5 lumen.
so the correct option is A.

A cyclotron in which protons are accelerated has a flux density 1.57T. The variation of frequency of electric field is (in Hz) 

  1. $4.8 \times 10 ^ { 8 }$

  2. $8.4 \times 10 ^ { 8 }$

  3. $2.5 \times 10 ^ { 7 }$

  4. $4.8 \times 10 ^ { 6 }$


Correct Option: C

The electric field potential in space has the form $V(x,y,z)=-2xy+3yz^{-1}$. The electric field intensity $\vec E$ magnitude at the point (-1,1,2) is

  1. $2 \sqrt{86} units$

  2. $2\sqrt{163} units$

  3. $\sqrt{163} units$

  4. $ \sqrt{86} units$


Correct Option: A

An iron rod of volume ${ 10 }^{ -4 }{ m }^{ 3 }$ and relative permeability 1000 is placed inside a long solenoid would with. 5 turn ism. If a current of 0.5 A is passed through the solenoid, then the magnetic moment of the rod is:

  1. 10 ${ Am }^{ 2 }$

  2. 15 ${ Am }^{ 2 }$

  3. 20 ${ Am }^{ 2 }$

  4. 25 ${ Am }^{ 2 }$


Correct Option: D

Unit of magnetic flux density is 

  1. $weber/metre$

  2. $weber$

  3. $weber/m^{2}$

  4. $ampere/m$


Correct Option: C

Current in a circular coil having negligible resistance and inductance 0.1 H is increasing at the rate of $1 As^{-1}$. The power generated in the coil when the magnetic flux linked with it is 0.1 Wb will be:-

  1. 0.05 W

  2. 0.1W

  3. 1 W

  4. 10 W


Correct Option: B

The magnetic flux density at a point distant $d$ from a long straight current carrying conductor is $B$, then its value at distance $d/2$ will be:

  1. $4B$

  2. $2B$

  3. $B/2$

  4. $B/4$


Correct Option: B
Explanation:

Flux density, B $=\dfrac{\phi}{A}$
$B _A=\dfrac{\mu _0 I}{2\pi d}=B$
$=\dfrac{\phi}{A}$
$B _A=\dfrac{\mu _0 I}{2\pi \dfrac{d}{2}}=2\dfrac{\mu _0 I}{2\pi d}$
$B _B=2\times B$
$B _B=2B$

The magnetic needle of a tangent galvanometer is deflected at an angle $30$ due to a magnet. The horizontal component of earth's magnetic field $0.34\times 10^{-4}T$ is along the plane of the coil. The magnetic intensity is:

  1. $1.96\times 10^{-4}T$

  2. $1.96\times 10^{-5}T$

  3. $1.96\times 10^{4}T$

  4. $1.96\times 10^{5}T$


Correct Option: B
Explanation:

The correct option is B.


Given,

$B=0.34\times10^{-4}T$

Deflected angle$\theta=30^0$

So magnetic intensity is $Btan 30^0$

$=0.34\times10^{-4}T\times\dfrac{1}{\sqrt3}$

$=1.96\times10^{-5}T$

Where,$tan 30^0=\dfrac{1}{\sqrt3}$, and $\sqrt3=1.73$c