Tag: magnetic effects of current and magnetism

Questions Related to magnetic effects of current and magnetism

A magnet of magnetic moment $50\hat{i} A-m^2$ is placed along x- axis in a magnetic field$ \overrightarrow {B} =( 0.5 \hat{i} + 3.0 \hat{j})$ tesla. The torque acting on the magnet is 

physics magnetic effects of current and magnetism the bar magnet magnetic field due to bar magnet intensity of magnetic field and torque on a bar magnet

  1. $175 \hat{k} N-m$

  2. $75 \hat{k} N-m$

  3. $150 \hat{k} N-m$

  4. $25 \sqrt{37}\hat{k} N-m$

Show answer
Correct Option: C
Explanation:

Given,

Magnetic field $\vec{B}\,=\,0.5\hat{i}\,+\,3.0\hat{j}\,\,T$

Magnetic moment $\mu =50\hat{i}\,\,A{{m}^{2}}$

Torque on magnet  $\tau $

$\tau =\mu \times \vec{B}\,\,=\,\,50\hat{i}\,\times \,(0.5\hat{i}\,+\,3.0\hat{j}\,)$

$\tau =\,150\hat{k}\,\,N-m$

Hence, Torque experiences by the magnet present in the magnetic field, $\tau =\,150\hat{k}\,\,N-m$ 

A bar magnet of dipole moment M is initially parallel to a magnetic field of induction B. The angle through which it should be rotated so that the torque acting on it is half the maximum torque is _____.

physics magnetic effects of current and magnetism the bar magnet magnetic field due to bar magnet intensity of magnetic field and torque on a bar magnet

  1. $90^0$

  2. $60^0$

  3. $45^0$

  4. $30^0$

Show answer
Correct Option: D
Explanation:

$\tau=MXB=MBsinQ$

At maximum torque the Q is $90^o$ 
$\tau=MBsin(90^o)=MB$----------------1

At the half of maximum torque,
$\dfrac{\tau}{2}=MXB=MBsinT$-----------------2

1 to 2
${\tau/2}{\tau}=\dfrac{MBsinT}{MB}$
$sinT=\dfrac{1}{2}$
$T=30^o$

A magnetic dipole of dipole moment $10(\hat{i}+\hat{j}+\hat{k})$ is placed in a magnetic field $0.6\hat{i}+0.4\hat{j}+0.5\hat{k}$, force acting on the dipole is :-

physics magnetic effects of current and magnetism the bar magnet magnetic field due to bar magnet intensity of magnetic field and torque on a bar magnet

  1. $\hat{i}-\hat{j}-2\hat{k}$

  2. $\hat{i}+\hat{j}+2\hat{k}$

  3. $Zero$

  4. $None\ of\ these$

Show answer
Correct Option: A
Explanation:

Given that,

Dipole moment $m=10\left( \hat{i}+\hat{j}+\hat{k} \right)$

Magnetic field $B=0.6\hat{i}+0.4\hat{j}+0.5\hat{k}$

We know that,

The force is

  $ \tau =m\times B $

 $ \tau =\left( 10\hat{i}+10\hat{j}+10\hat{k} \right)\times \left( 0.6\hat{i}+0.4\hat{j}+0.5\hat{k} \right) $

 $ \tau =\hat{i}-\hat{j}-2\hat{k} $

Hence, the force acting on the dipole is $\hat{i}-\hat{j}-2\hat{k}$

 

A current $i$ is flowing in a circular conductor of radius $r$, it is lying in a uniform magnetic field $B$ such that its plane is normal to $B$. The magnetic force acting on the loop will be_

physics magnetic effects of current and magnetism the bar magnet magnetic field due to bar magnet intensity of magnetic field and torque on a bar magnet

  1. $zero$

  2. $\pi irB$

  3. $2 \pi irB$

  4. $irB$

Show answer
Correct Option: A
Explanation:
Lets consider a small arc of length $dl$ of the circular loop
The magnetic force acting on the loop will be,
$\vec F=i(d\vec l\times \vec B)$ .. . .  ..  . . .. (1)
the force acting towards the center.
When the magnetic field $B$ is perpendicular to the $dl$, the angle between them is $90^0$.
$\theta=90^0$
From equation (1),
$\vec F=i|d\vec l||\vec B|sin\theta=idlB$
But the similar element of arc is opposite to the consider arc, so the current is also in the opposite direction and the force acting on the loop is now towards outward, both force cancel each other and the net force acting on the loop will be zero.
The correct option is A.

If a bar magnet is kept perpendicular in a magnetic field of unit magnetic induction then its magnetic moment is equal to:

physics magnetic effects of current and magnetism the bar magnet magnetic field due to bar magnet intensity of magnetic field and torque on a bar magnet

  1. magnetic flux

  2. torque

  3. pole strength

  4. magnetic flux density

Show answer
Correct Option: B
Explanation:

From the given question, 

$B=1T$
$\theta=90^0$
The torque acting on the bar magnet is given by
$\tau=MBsin\theta=M\times 1\times sin90^0$
$\tau=M$
The magnetic moment is equal to the torque.
The correct option is B.

The small magnets each of magnetic moment $10A-{ m }^{ 2 }$ are placed end on position 0.1m apart from their centres.The force acting between them is :

physics magnetic effects of current and magnetism the bar magnet magnetic field due to bar magnet intensity of magnetic field and torque on a bar magnet

  1. $0.6\times { 10 }^{ 7 }N$

  2. $0.06\times { 10 }^{ 7 }N$

  3. $0.6N$

  4. $0.06N$

Show answer
Correct Option: C
Explanation:

Given,


$M _1=M _2=10Am^2$


$r=0.1m$

The force acting between the magnet is given by,

$F=\dfrac{\mu _0}{4\pi }.\dfrac{6M _1M _2}{r^4}$

$F=10^{-7}\times \dfrac{6\times 10\times 10}{(0.1)^4}$

$F=0.6N$

The correct option is C.

A magnetic needle lying parallel to a magnetic field requires W unit of work to turn it through $60^0$. The torque needed to maintain the needle in this position will be 

physics magnetic effects of current and magnetism the bar magnet magnetic field due to bar magnet intensity of magnetic field and torque on a bar magnet

  1. $\sqrt3W$

  2. W

  3. $(\sqrt3/2)W$

  4. 2W

Show answer
Correct Option: A
Explanation:
Work done to rotate the needle$=$Potential energy of needle$=$W
If M$=$Magnetic dipole moment of the needle and B$=$magnetic field then:
$W=MB(\cos\theta _1-\cos\theta _2)$ (where $\theta _1=0^o$ and $\theta _2=60^o$)
$\Rightarrow W=MB(1-1/2)=\dfrac{MB}{2}$ or $MB=2W\rightarrow (1)$
So restoring torque acting on the needle is given by:
$\tau =M\times B=MB\sin 60^o$(In magnitude)
$\Rightarrow \tau =\dfrac{\sqrt{3}}{2}MB$
$\Rightarrow \tau =\dfrac{\sqrt{3}}{2}2W=\sqrt{3}W$.

A bar magnet having centre O has a length of 4 cm. Point $P _1$ is in the broad side-on and $P _2$ is in the end side-on position with $OP _1=OP _2=10$ metres. The ratio of magnetic intensities H at $P _1$ and $P _2$ is

physics magnetic effects of current and magnetism the bar magnet magnetic field due to bar magnet intensity of magnetic field and torque on a bar magnet

  1. $H _1:H _2=16:100$

  2. $H _1:H _2=1:2$

  3. $H _1:H _2=2:1$

  4. $H _1:H _2=100:16$

Show answer
Correct Option: B

A magnet of moment  $80A{m^2}$ is placed in a uniform magnetic field of induction $1.8 \times {10^{ - 5}}T$. If each pole of the magnet experiences a force of  $25 \times {10^{ - 3}}N$, the length of the magnet is:

physics magnetic effects of current and magnetism the bar magnet magnetic field due to bar magnet intensity of magnetic field and torque on a bar magnet

  1. 0.292cm

  2. 5.76cm

  3. 0.362cm

  4. 2.262cm

Show answer
Correct Option: B

Which of the following cannot be the shape of the path of a charged particle moving in a uniform magnetic field?

physics magnetic effects of current and magnetism the bar magnet magnetic field due to bar magnet intensity of magnetic field and torque on a bar magnet

  1. straight line

  2. parabolic

  3. circular

  4. helical

Show answer
Correct Option: C
Explanation:

It will be a circular path with radius

$r=\left( \frac { mc }{ qB }  \right) $

and time period of

$T=\left( 2\times pi\times \frac { m }{ qB }  \right) $

This you can get from study of force on moving charge in magnetic field.

This is similar to cyclotron except that, in cyclotron, there is presence of electric field in addition to magnetic field. Hence in cyclotron, the radius of circular path keeps on increasing as speed of charge increases.