Magnetic Intensity

Q. An electric dipole has fixed dipole moment $\overrightarrow{p}$, which makes angle $\theta$ with respect to x-axis. When subjected to an electric field $\overrightarrow{E_1}=E\hat{i}$, it experiences a torque $\overrightarrow{T_1}=\tau \hat{k}$. When subjected to another electric field $\overrightarrow{E_2}=\sqrt{3}{E}_1\hat{j}$, it experiences a torque $\overrightarrow{T_2}=-\overrightarrow{T_1}$. The angle $\theta$ is

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

Q. The electric field and the potential of an electric dipole vary with distance r respectively as:

1. $\frac{1}{r^2}$ and $\frac{1}{r^3}$
2. $\frac{1}{r}$ and $\frac{1}{r^2}$
3. $\frac{1}{r^2}$ and $\frac{1}{r}$
4. $\frac{1}{r^3}$ and $\frac{1}{r^2}$

Q. The percentage increase in magnetic field, when the space within a current carrying toroid is filled with aluminium. The susceptibility of aluminium is $2.1\times {10}^{-5}$.

1. $1.1\times {10}^{-3}$
2. $2.1\times {10}^{-3}$
3. $3.1\times {10}^{-3}$
4. $4.1\times {10}^{-3}$

Q.

The magnetic susceptibility of a medium is $0.825$. Its relative permeability is

1. $1.825$

2. $2.085$

3. $4.885$

4. $0.825$

Q. The approximate value of magnetic field due to a dipole of magnetic moment $1.2{\text{Am}}^2$ at a point $1\text{m}$ away from it in a direction making an angle of ${60}^{\circ }$ with the dipole axis is

1. $0.8\times {10}^{-7}\text{T}$
2. $1.6\times {10}^{-7}\text{T}$
3. $2.4\times {10}^{-7}\text{T}$
4. $3.2\times {10}^{-7}\text{T}$

Q.

$1Gauss$ is equal to

1. ${10}^{4}T$

2. ${10}^{-4}T$

3. ${10}^{3}T$

4. none of these

Q. If a long hollow thin copper pipe carries a direct current, the magnetic field associated with the current will be present

$[$0.77 Mark$]$

1. Only inside the pipe
2. Only outside the pipe
3. Neither inside nor outside the pipe
4. Both inside and outside the pipe

Q. A toroid of mean radius $16\text{cm}$ has $1000$ turns of wire closely wounded on a ferromagnetic core of relative permeability $400$. What is the magnetic induction $B$ within the core for a magnetizing current of $1\text{A}$ ?

1. $0.00125\text{T}$
2. $0.00250\text{T}$
3. $1\text{T}$
4. $0.5\text{T}$

Q. The $\text{B-H}$ curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with $1000\text{turns/cm}$. The current that should be passed in the solenoid to demagnetize a ferromagnet completely is:

1. ${10}^{-1}\text{A}$
2. ${10}^{-2}\text{A}$
3. ${10}^{-3}\text{A}$
4. ${10}^{-4}\text{A}$

Q. The intensity of magnetic field is H and moment of magnet is M. The maximum potential energy is

1. MH
2. 2 MH
3. 3 MH
4. 4 MH

Q. At time $t=0$ magnetic field of $1000\text{G}$ is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to $500\text{G}$, in the next $5\text{s}$, then induced $EMF$ in the loop is:

1. $56\mu \text{V}$
2. $28\mu \text{V}$
3. $48\mu \text{V}$
4. $36\mu \text{V}$

Q.
A square frame with side length $l$ has total resistance $R$. It is being pulled with speed $v$ out of region of uniform magnetic field $B$. Moment when left corner is at distance $x$ inside field, the force required to pull frame at constant speed $v$ is

1. $\frac{2B^2{x}^{2}v}{2R}$
2. $\frac{3B^2{x}^{2}v}{2R}$
3. $\frac{2B^2{x}^{2}v}{R}$
4. $\frac{4B^2{x}^{2}v}{R}$

Q.

In which of the following systems of unit, Weber is the unit of magnetic flux

1. CGS

2. SI

3. MKS

4. None of the option

Q.

A symmetric star shaped conducting wire loop is carrying a steady state current $I$ as shown the figure. The distance between the diametrically opposite vertices of the star is $4a$. The magnitude of the magnetic field at the center of the loop is

1. $\frac{{\mu }_{0}I}{4\pi a}6[\sqrt{3}-1]$

2. $\frac{{\mu }_{0}I}{4\pi a}3[\sqrt{3}-1]$

3. $\frac{{\mu }_{0}I}{4\pi a}6[\sqrt{3}+1]$

4. $\frac{{\mu }_{0}I}{4\pi a}3[2-\sqrt{3}]$

Q.

A rod is inserted as the core in the current-carrying solenoid of the previous problem. (a) What is the magnetic intensity H at the centre ? (b) If the magnetization I of the core is found to be 0.12 A $m^{-1}$ find the susceptibility of the material of the rod. (c) Is the material paramagnetic, diamagnetic or ferromagnetic ?

Q.

Magnetic susceptibility of a material is$499$ &${\mu }_0=4\pi \times {10}^{-7}SIunit$. Then find${\mu }_r$

1. $500$

2. $400$

3. $300$

4. $200$

Q. The magnetic dip angle at two places are ${30}^{\circ }$ and ${45}^{\circ }$. The ratio of horizontal components of earths magnetic field at the two places is-

1. $1:\sqrt{2}$
2. $\sqrt{3}:\sqrt{2}$
3. $\sqrt{2}:1$
4. $\sqrt{3}:1$

Q.

How do you know the permeability?

Q.

Why does a compass needle get deflected when brought closer to a bar magnet?

Q. The variation of magnetic susceptibility $\left(\chi \right)$ with temperature $\left(T\right)$ for diamagnetic substances is best represented by,

1. 
2. 
3. 
4. 

Q. $C.G.S.$ unit of magnetic field intensity is:

1. Tesla
2. Gauss
3. Weber
4. None of these

Q. A demagnetize a small ferromagnet, a current of $2A$ is required to be passed in a solenoid of length $20cm$ and number of turns $100$. The coercivity of the magnet is:

1. $5000A{m}^{-1}$
2. $1000A{m}^{-1}$
3. $1250A{m}^{-1}$
4. $3750A{m}^{-1}$

Q. Two toroidal solenoids are wound around the same pipe so that the magnetic field of one passes through the turns of the other. Solenoid $1$ has $700$ turns and solenoid $2$ has $400$ turns. When the current in solenoid $1$ is $6.52A$, the average flux through each turn of solenoid $2$ is $0.0320Wb$. When the current in solenoid $2$ is $2.54A$, what is the average flux through each turn of solenoid $1$?

1. $7.12\times {10}^{-3}Wb$
2. $9.12\times {10}^{-9}Wb$
3. $5.12\times {10}^{-7}Wb$
4. $7.12\times {10}^{-13}Wb$

Q.

$1Gauss$ is equal to

1. ${10}^{4}T$

2. ${10}^{-4}T$

3. ${10}^{3}T$

4. none of these

Q. There are two metallic loops of radii $0.2\text{m}$ and $0.5\text{m}$. The smaller loop is placed within the bigger one. Calculate the magnitude of the magnetic flux through the bigger loop, if the field is directed into the page of the loop and enclosed by the smaller loop. The strength of the magnetic field is $2.4\text{T}$.

1. $0.3\text{weber}$
2. $0.03\text{weber}$
3. $3\text{weber}$
4. $0.003\text{weber}$

Q.

A bar magnet of pole strength 50 A.m. is cut into 10 equal parts parallel to its axial line. The intensity of magnetisation of each piece will be :

1. $\frac{1}{10}$th of initial value
2. same of initial value
   
3. half of initial value
   
4. 10 times initial value

Q. $\left[\frac{Permeability}{Permittivity}\right]$will have the dimensions of :

1. $M^0{L}^0{T}^0{A}^0$
2. $M^2{L}^2{T}^4{A}^2$
3. $M^2{L}^4{T}^{-6}{A}^{-4}$
4. $M^{-2}{L}^{-4}{T}^6{A}^4$

Q. The magnetic moment of a dipole is 2 Am${}^2$. Magnetic induction in air at a distance of 10 cm from the dipole on a line making an angle of ${60}^0$ with the axis of dipoles is :

1. $\sqrt{7}/2\times {10}^{-4}T$
2. $\sqrt{7}\times {10}^{-4}T$
3. $\sqrt{7}/2\times {10}^{-5}T$
4. $\sqrt{7}\times {10}^{-5}T$

Q. A magnetic field of $2\times {10}^{-2}T$ acts at right angles to a coil of area $100c{m}^2$, with $50$ turns. The average e.m.f. induced in the coil is $0.1V$, when it is removed from the field in $t$ $sec$. The value of $t$ is

1. $10s$
2. $0.1s$
3. $0.01s$
4. $10s$

Q.

Two short bar magnets each of magnetic moment $10A{m}^2$ are kept at the two opposite corners of a square of side 1m with magnetic moments parallel. The field strength at any one of the other corners is :

1. $1\times {10}^{-6}T$
2. $2\times {10}^{-6}T$
3. $4\times {10}^{-6}T$
4. $3\times {10}^{-6}T$