Solenoid Core in Magnetic Field

Q. An iron rod of susceptibility $599$ is subjected to a magnetizing field of $1200{\text{Am}}^{-1}$. The permeability of the material of the rod is :

Take, ${\mu }_0=4\pi \times {10}^{-7}{\text{TmA}}^{-1}$

1. $2.4\pi \times {10}^{-3}{\text{TmA}}^{-1}$
2. $2.4\pi \times {10}^{-5}{\text{TmA}}^{-1}$
3. $2.4\pi \times {10}^{-7}{\text{TmA}}^{-1}$
4. $2.4\pi \times {10}^{-4}{\text{TmA}}^{-1}$

Q.

What is the unit of magnetic intensity?

Q. An iron rod of susceptibility $599$ is subjected to a magnetising field of $1200{\text{Am}}^{-1}$. The permeability of the material of the rod is :$({\mu }_0=4\pi \times {10}^{-7}{\text{T mA}}^{-1})$

1. $2.4\pi \times {10}^{-5}{\text{T mA}}^{-1}$
2. $2.4\pi \times {10}^{-7}{\text{T mA}}^{-1}$
3. $2.4\pi \times {10}^{-4}{\text{T mA}}^{-1}$
4. $8\times {10}^{-5}{\text{T mA}}^{-1}$

Q. 75.Magnetic needle oscillates in a horizontal plane with the time period t at a place with angle of dip 60 degree when the same needle is made to oscillate in a vertical plane coinciding with the magnetic meridian its period will be 1)T/2 2)T 3)2T 4)2T

Q. The value of aluminum's susceptibility is $2.2\times {10}^{-5}$. The percentage increase in the magnetic field, if space within a current carrying toroid, is filled with aliminum, is $\frac{x}{{10}^4}$. Then, the value of $x$ is

Q. A bar magnet is held perpendicular to a uniform magnetic field. If the couple acting on the magnet is to be halved by rotating it, then the angle by which it is to be rotated is

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

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

1. $175\hat{k}N-m$
2. $150\hat{k}N-m$
3. $75\hat{k}N-m$
4. $25\sqrt{37}\hat{k}N-m$

Q. A bar magnet when placed at an angle of ${30}^{\circ }$ to the direction of magnetic field induction of $5\times {10}^{-2}T$, experiences a moment of couple $25\times {10}^{-6}N-m$. If the length of the magnet is 5 cm its pole strength is

1. $5\times {10}^{-2}A-m$
2. $2A-m$
3. $5A-m$
4. $2\times {10}^{-2}A-m$

Q.

A magnet of total magnetic moment ${10}^{-2}\hat{i}A-m^2$ is placed in a time varying magnetic field, $B\hat{i}\left(cos\omega t\right)$ where$B=1Tesla$ and $\omega =0.125rad/s$ . The work done for reversing the direction of the magnetic moment at $t=1s$, is

1. $0.007J$

2. $0.02J$

3. $0.01J$

4. $0.028J$

Q. A bar magnet of magnetic moment ${10}^4\text{J/T}$ is free to rotate in a horizontal plane. The work done in rotating the magnet slowly from a direction parallel to a horizontal magnetic field of $4\times {10}^{-5}\text{T}$ to a direction ${60}^{\circ }$ from the field will be

1. $0.2\text{J}$
2. $2.0\text{J}$
3. $4.18\text{J}$
4. $4.2\times {10}^2\text{J}$

Q. The pole strength of a bar magnet is 48 ampere - metre and the distance between its poles is 25 cm. The moment of the couple by which it can be placed at an angle of ${30}^{\circ }$ with the uniform magnetic intensity of flux density 0.15 Newton / ampere – metre will be

1. None of the above
2. 8 Newton - metre
3. 12 Newton - metre
4. 0.9 Newton - metre

Q. The work done in rotating a magnet of magnetic moment $2A-m^2$ in a magnetic field of $5\times {10}^{-3}T$ from the direction along the magnetic field to opposite direction to the magnetic field, is

1. $2\times {10}^{-2}J$
2. ${10}^{-2}J$
3. Zero
4. $10J$

Q. A magnet of length 0.1 m and pole strength ${10}^{-4}A.m$ is kept in a magnetic field of $30Wb/m^2$ at an angle ${30}^{\circ }$. The couple acting on it is ……… $\times {10}^{-4}Nm$.

1. 6
2. 7.5
3. 1.5
4. 3

Q. A magnet is suspended in the magnetic meridian with an untwisted wire. The upper end of wire is rotated through ${180}^{\circ }$ to deflect the magnet by ${30}^{\circ }$ from magnetic meridian. When this magnet is replaced by another magnet, the upper end of wire is rotated through ${270}^{\circ }$ to deflect the magnet ${30}^{\circ }$ from magnetic meridian. The ratio of magnetic moments of magnets is

1. 1 : 5
2. 1 : 8
3. 5 : 8
4. 8 : 5

Q. A magnet of magnetic moment $2J{T}^{-1}$ is aligned in the direction of magnetic field of 0.1 T. What is the net work done to bring the magnet normal to the magnetic field

1. 0.1 J
2. 0.2 J
3. 2 J
4. 1 J

Q. A bar magnet of length $10\text{cm}$ and pole strength $2\text{Am}$ makes an angle ${60}^{\circ }$ with a uniform magnetic field of induction $B=50\text{T}.$ The couple acting on it is-

1. $20\sqrt{3}\text{Nm}$
2. $10\sqrt{3}\text{Nm}$
3. $\sqrt{3}\text{Nm}$
4. $5\sqrt{3}\text{Nm}$

Q. A current carrying circular loop is placed in a uniform magnetic field $B$, the potential energy is minimum when the magnetic moment of the loop is

1. $\text{Parallel to}B$
2. $\text{Perpendicular to}B$
3. $\text{Inclined at an angle of}{45}^{\circ }\text{to}B$
4. $\text{Anti-parallel to}B$

Q. The torque required to keep a magnet of length $20\text{cm}$ at ${30}^{\circ }$ to a uniform magnetic field is $2\times {10}^{-5}\text{Nm}$. The magnetic force on each pole is-

1. $2\times {10}^{-6}\text{N}$
2. $2\times {10}^{-5}\text{N}$
3. $2\times {10}^{-4}\text{N}$
4. $2\times {10}^{-3}\text{N}$

Q. An ideal solenoid having 40 turns ${\text{cm}}^{-1}$ has an aluminum core, and carries a current of $2.0\text{A}$. Calculate the magnetic field $B$ at the centre. The susceptibility $\chi$ of aluminium $=2.3\times {10}^{-5}$.

1. $3.2\pi \times {10}^{-4}\text{T}$
2. $1.6\pi \times {10}^{-4}\text{T}$
3. $0.8\pi \times {10}^{-4}\text{T}$
4. $\pi \times {10}^{-4}\text{T}$

Q. A bar magnet of moment $\overrightarrow{M}=\hat{i}+\hat{j}$ is placed in a magnetic field induction $\overrightarrow{B}=3\hat{i}+4\hat{j}+4\hat{k}$. The torque acting on the magnet is-

1. $\hat{i}+\hat{j}+\hat{k}$
2. $\hat{i}-\hat{j}$
3. $\hat{i}+\hat{k}$
4. $4\hat{i}-4\hat{j}+\hat{k}$

Q. A wire of length $314\text{cm}$ is used to make a toroid of cross- sectional radius $2\text{cm}$. Find the magnetic field at the inner core of the toroid having average radius of $50\text{cm}$ and current flowing through it is $2\text{A}$.
[wires are closely wounded]

1. $2\times {10}^{-5}\text{T}$
2. $0.5\times {10}^{-5}\text{T}$
3. $1\times {10}^{-4}\text{T}$
4. $0.25\times {10}^{-3}\text{T}$

Q. The couple acting on a bar magnet of pole strength $4\text{Am}$, when placed in a uniform magnetic field of intensity $10\sqrt{3}{\text{Am}}^{-1}$, such that axis of the magnet makes an angle ${60}^{\circ }$ with the direction of the field is $80\times {10}^{-6}\text{Nm}$. Find the distance between the poles of the magnet is,

1. $0.6\mu \text{m}$
2. $0.3\mu \text{m}$
3. $1.3\mu \text{m}$
4. $0.9\mu \text{m}$

Q. The magnetic susceptibility of a medium is $–0.08$, what will be its relative permeability?

1. $1.8$
2. $1.08$
3. $0.08$
4. $0.92$

Q.

Why is the permeability important?

Q. A small bar magnet of moment M is placed in a uniform field H. If magnet makes an angle of ${30}^{\circ }$ with field, the torque acting on the magnet is

1. MH
2. $\frac{MH}{2}$
   
3. $\frac{MH}{3}$
   
4. $\frac{MH}{4}$

Q.

The magnetic field inside a long solenoid having 50 turns $c{m}^{-1}$ is increased from 2.5 $\times {10}^{-3}$T to 2.5 T when an iron core of cross-sectional area 4 $c{m}^2$ is inserted into it. Find (a) the current in the solenoid, (b) the magnetization I of the core and (c) the Pole strength developed in the core.

Q. A bar magnet is held perpendicular to a uniform magnetic field. If the couple acting on the magnet is to be halved by rotating it, then the angle by which it is to be rotated is

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q. An iron rod of volume ${10}^{-4}{\text{m}}^3$ and relative permeability $1000$ is placed inside a long solenoid wound with $5\text{turns/cm}$. If a current of $0.5\text{A}$ is passed through the solenoid, find the magnetic moment of the rod.

1. $15{\text{Am}}^2$
2. $20{\text{Am}}^2$
3. $25{\text{Am}}^2$
4. $30{\text{Am}}^2$

Q. A current carrying loop whose magnetic moment is at ${30}^{\circ }$ with a uniform external magnetic field of $0.16\text{T}$ experiences a torque of magnitude $0.032\text{Nm}$. If the coil is free to rotate, its potential energies when it is in stable and unstable equilibrium are respectively

1. $-0.064\text{J},-0.064\text{J}$
2. $+0.064\text{J},-0.064\text{J}$
3. $+0.064\text{J},+0.064\text{J}$
4. $-0.064\text{J},+0.064\text{J}$

Q. The magnetic moment of a solenoid of 100 turns carry a current of 1 A and having an area of 0.01 $m^2$ is

1. 20 $A{m}^2$
2. 1 $A{m}^2$
3. 0.1 $A{m}^2$
4. Data insufficient