Magnetic Moment

Q.

What are coercivity and retentivity?

Q. An iron rod of length L and magnetic moment M is bent in the form of a semicircle. Now its magnetic moment will be

1. $\frac{2M}{\pi }$
2. $\frac{M}{\pi }$
3. M
4. $M\pi$

Q.

An electric dipole with dipole moment $\frac{P_0}{\sqrt{2}}(\hat{i}+\hat{j})$ is held fixed at the origin O in the presence of an uniform electric field of magnitude $E_0$. If the potential is constant on a circle of radius R centered at the origin as shown in the figure, then the correct statement (s) is/are : (${\in }_0$ is permittivity of free space. R >> dipole size)

1. The magnitude of total electric field on any two points of the circle will be same.

2. Total electric field at point A is ${\overrightarrow{E}}_A=\sqrt{2}{E}_0(\hat{i}+\hat{j})$

3. $R={\left(\frac{P_0}{4\pi {\epsilon }_0{E}_0}\right)}^{1/3}$

4. Total electric field at point B is ${\overrightarrow{E}}_B=0$

Q. $\text{Statement I}:$ The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet.
$\text{Statement II}:$ At high temperature, the domain wall area of a ferromagnetic substance increases.

In the light of the above statements, choose the most appropriate answer from the options given below :

1. $\text{Statement I}$ is false, but $\text{Statement II}$ is true.
2. Both $\text{Statement I}$ and $\text{Statement II}$ are true.
3. $\text{Statement I}$ is true, but $\text{Statement II}$ is false.
4. Both $\text{Statement I}$ and $\text{Statement II}$ are false.

Q. A circular coil of radius ‘r’ carries a current I. At what distance from centre on its axis the magnetic field is $\frac{1}{27}th$ of its value at the centre?

1. $2\sqrt{2}r$
2. $\sqrt{3}r$
3. $2\sqrt{3}r$
4. $\sqrt{5}r$

Q.

A non conducting disc of radius R is rotating about an axis passing through its centre and perpendicular to its plane with an angular velocity $\omega$. Charge q is uniformly distributed over its surface. The magnetic moment of the disc is

1. $\frac{1}{4}q\omega R^2$

2. $\frac{1}{2}q\omega R$

3. $q\omega R$

4. $\frac{1}{2}q\omega R^2$

Q. The electric potential due to dipole at a general point which is at distance $r$ from center of the dipole is

1. $V=\frac{k(\overrightarrow{p}\cdot \overrightarrow{r})}{r^3}$
2. $V=\frac{k(\overrightarrow{p}\cdot \overrightarrow{r})}{r^2}$
3. $V=\frac{k(\overrightarrow{p}\cdot \overrightarrow{r})}{r}$
4. $V=\frac{k(\overrightarrow{p}\cdot \overrightarrow{r})}{r^4}$

Q. The effective length of a magnet is 31.4 cm and its pole strength is 0.5 Am. The magnetic moment, if it is bent in the form of a semicircle will be

1. $0.01A{m}^2$
2. $0.2A{m}^2$
3. $0.1A{m}^2$
4. $1.2A{m}^2$

Q. A positively charged particle having charge $q$ and mass $m$ moving with velocity $v_0\hat{i}$ enters a region in which magnetic field $\overrightarrow{B}=-B_0\hat{k}$ exists. The magnetic field region extends from $x=0$ to $x=d$. Then the time spent by the particle in magnetic field if $d$ is equal to $\frac{1.5mv}{qB}$

1. $\frac{\pi m}{qB}$
2. $\frac{2\pi m}{qB}$
3. $\frac{2\pi m}{3qB}$
4. $\frac{\pi m}{4qB}$

Q. A point charge of $0.1\text{C}$ is placed on the circumference of a non-conducting ring of radius $1m$ which is rotating with a constant angular acceleration of $1{\text{rad/sec}}^2$. If ring starts it's motion at $t=0$, the magnetic field at the centre of the ring at $t=10$ sec is ${10}^{-x}$. Then $x$ is

Q. If a proton enters a region of uniform magnetic field with velocity $v$ in a direction perpendicular to the magnetic field, then the time period of revolution is $T$. If proton enters with velocity $2v$, the time period will be

1. $T$
2. $2T$
3. $3T$
4. $4T$

Q. Two short bar magnets each of magnetic moment $M$ are placed as shown in the figure. The magnetic field at the point $P$ will be

1. $\frac{{\mu }_0}{4\pi }\frac{2\sqrt{2}M}{d^3}$ towards right
2. $\frac{{\mu }_0}{4\pi }\frac{2\sqrt{2}M}{d^3}$ towards left
3. $\frac{{\mu }_0}{4\pi }\frac{2M}{d^3}$ towards left
4. $\frac{{\mu }_0}{4\pi }\frac{2M}{d^3}$ towards right

Q. A bar magnet of magnetic moment $3.0A-m^2$ is placed in a uniform magnetic induction field of $2\times {10}^{-5}T$. If each pole of the magnet experiences a force of $6\times {10}^{4}N$, the length of the magnet is

1. 0.5 m
2. 0.3 m
3. 0.2 m
4. 0.1 m

Q. A square loop $\text{OABCO}$ of side length $l$ carries a current $i$. It is placed as shown in the figure. The magnetic moment of the loop will be :

1. $\frac{i{l}^2}{2}(\hat{i}-\sqrt{3}\hat{k})$
2. $i{l}^2(\hat{j}-\sqrt{2}\hat{i})$
3. $\frac{i{l}^2}{5}(\hat{j}-\sqrt{5}\hat{i})$
4. $\frac{i{l}^2}{2}(\hat{j}+\sqrt{3}\hat{i})$

Q. A long magnetic needle of length 2L, magnetic moment M and pole strength m units is broken into two pieces at the middle. The magnetic moment and pole strength of each piece will be

1. $M,\frac{m}{2}$
   
2. $\frac{M}{2},m$
   
3. $M,m$
4. $\frac{M}{2},\frac{m}{2}$
   

Q. A rod of length $l$ rotates with a uniform angular velocity $\omega$ about its perpendicular bisector. A uniform magnetic field $B$ exists parallel to the axis of rotation. The potential difference between the two ends of the rod is

1. $\text{Zero}$
2. $\frac{1}{2}Bl{\omega }^2$
3. $Bl{\omega }^2$
4. $2Bl{\omega }^2$

Q.

The combination of two bar magnets makes 10 oscillations per second in an oscillation magnetometer when like poles are tied together and 2 oscillation per second when unlike poles are tied together. Find the ratio of the magnetic moments of the magnets. Neglect any induced magnetism.

Q. A rod $\text{OPQ}$ is rotating with angular speed $\omega$ about point $O$ as shown in the figure. A uniform inward magnetic field $B$ exists perpendicular to the plane of the rod. Potential difference between points $P$ and $Q$ of the rod is -

1. $\frac{B\omega l^2}{2}$
2. $B\omega l^2$
3. Zero
4. $\frac{B\omega l^2}{8}$

Q. when 4 bar magnets of moments M, 2M, 3M, 4M are arranged to form a square with unlike poles at each corner then resul†an t magnetic moment is

Q. A particle moving with velocity $v$ having specific charge $\left(\frac{q}{m}\right)$ enters a region of magnetic field $B$ having width $d=\frac{3mv}{5qB}$ at angle ${53}^o$ to the boundary of magnetic field. Find the angle $\theta$ in the shown figure.

1. ${37}^{\circ }$
2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. None

Q. A short bar magnet is placed with its north pole pointing north. The neutral point is 10 cm away from the cemtre of the magnet.If B_H=0.4 G, calculate the magnetic moment of the magn

Q.

Considering that ${∆}_{°}>\mathrm{P}$, the magnetic moment (in BM) of ${\left[\mathrm{Ru}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{+2}$ would be

Q. A bar magnet of length $l$ and magnetic dipole moment $M$ is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be

1. $\frac{2}{\pi }M$
2. $\frac{M}{\pi }$
3. $M$
4. $\frac{3}{\pi }M$

Q. The magnetic moment of a magnet of length 10 cm and pole strength 4.0 Am will be

1. $1.6A{m}^2$
2. $0.4A{m}^2$
3. $20A{m}^2$
4. $8.0A{m}^2$

Q.

A long bar magnet has a pole strength of 10 Am. Find the magnetic field at a point on the axis of the magnet distance of 5 cm from the north pole of the magnet.

Q. A Charged sphere of mass $m$ and charge $q$ starts sliding from rest on a vertical fixed circular track of radius $R$ from the position as shown in figure. There exists a constant magnetic field in horizontal direction as shown in figure. The maximum force exerted by track on the sphere is:

1. $3mg+qB\sqrt{2gR}$
2. $mg+3qB\sqrt{gR}$
3. $2mg+qB\sqrt{gR}$
4. $2mg+3qB\sqrt{2gR}$

Q.

Figure shows some of the equipotential surfaces of the magnetic scalar potential. Find the magnetic field B at a point in the region.

Q. Force between two unit pole strength placed at a distance of one metre is

1. $\frac{{10}^{-7}}{4\pi }N$
   
2. ${10}^{-7}N$
   
3. $4\pi \times {10}^{-7}N$
4. 1 N

Q. As shown in the figure, a magnet is brought towards a fixed coil. Due to this, the induced emf, current and the charge are $E$, $I$ and $Q$ respectively. If the speed of the magnet is doubled, then which of the following statements is wrong?

1. $E$ increases.
2. $I$ increases.
3. $Q$ increases.
4. None of the above

Q.

At ${45}^{°}$ of the magnetic meridian angle of dip is $30°$ then find the angle of dip in a vertical plane at $45°$ ?

1. ${\tan }^{-1}\left(\frac{1}{\sqrt{6}}\right)$

2. ${\tan }^{-1}\left(\frac{1}{\sqrt{2}}\right)$

3. ${\tan }^{-1}\left(\frac{1}{\sqrt{4}}\right)$

4. ${\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)$