Tag: magnetic fields and electromagnetism

Questions Related to magnetic fields and electromagnetism

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

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. $\dfrac {2Q}{\in _{0}}$


Correct Option: A

The flux linked with a coil changes with time according to the equation $\phi$ = a$t^2$ +bt +c. Then SI unit of a is 

  1. Volt

  2. Volt/sec

  3. Volt.sec

  4. Weber


Correct Option: B
Explanation:

The unit of $\phi$ is Volt-sec.

Now $\phi=a t^{2}+bt+c$
To meet the dimension requirement $at^{2}$ must be Volt-sec.
$a$ must Volt/sec.

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. $0.8\ C$


Correct Option: B
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 $


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


Correct Option: B