Coupling

Q.

A vibration magnetometer placed in a magnetic meridian has a small bar magnet. The magnet executes oscillations with a time period of $2\sec$ in the earths horizontal magnetic field of $24$ microteslas. When a horizontal field of $18$ microteslas is produced opposite to the earths field by placing a current-carrying wire, the new time period of the magnet will be

1. $1\mathrm{s}$

2. $2\mathrm{s}$

3. $3\mathrm{s}$

4. $4\mathrm{s}$

Q. A hollow cylindrical wire carries a current $I$, having inner and outer radii $R$ and $2R$ respectively. Magnetic field at a point which $\frac{3R}{2}$ distance away from its axis is

1. $\frac{5{\mu }_{0}I}{18\pi R}$
2. $\frac{{\mu }_{0}I}{36\pi R}$
3. $\frac{5{\mu }_{0}I}{36\pi R}$
4. $\frac{5{\mu }_{0}I}{9\pi R}$

Q.

A conducting circular loop is placed in a uniform magnetic field $B=0.025T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $1mm/s$. What is the induced emf in the loop if the radius is $2cm$?

Q. Two coils of self inductance $L_1$and $L_2$ are placed closer to each other so that total flux in one coil is completely linked with other. If is mutual inductance between them, then

1. M = L₁ / L₂
2. M = L₁L₂
3. M = √L₁L₂
4. M = (L₁L₂)²

Q. A long, straight wire, of radius $a$, carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire, at distances $\frac{a}{3}\text{and}2a,$ respectively from the axis of the wire, is:

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

Q. A conducting circular loop is placed in a uniform magnetic field $0.04\text{T}$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at a uniform rate of $2\text{mm/s}$. The induced emf in the loop, when the radius is $2\text{cm}$, is:

1. $1.6\pi \mu \text{V}$
2. $3.2\pi \mu \text{V}$
3. $4.8\pi \mu \text{V}$
4. $0.8\pi \mu \text{V}$

Q. In a vibration magnetometer, the time period of a bar magnet oscillating in horizontal component of earth's magnetic field is 2 sec. When a magnet is brought near and parallel to it, the time period reduces to 1 sec. The ratio H/F of the horizontal component H and the field F due to magnet will be

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

Q. An infinitely long hollow conducting cylinder with inner radius $\frac{R}{2}$ and outer radius R carries a uniform current density along its length. The magnitude of the magnetic field $|B|$ as a function of the radial distance $r$ from the axis is best represented by

1. 
2. 
3. 
4. 

Q. A current loop having two circular arcs joined by two radial line as shown in figure. It carries a current of $10\text{A}$. The magnetic field at point $\text{O}$ will be close to

1. $1.0\times {10}^{-5}\text{T}$
2. $1.0\times {10}^{-7}\text{T}$
3. $1.5\times {10}^{-7}\text{T}$
4. $1.5\times {10}^{-5}\text{T}$

Q. Magnetic field of earth is $0.3\text{G}$. A magnet is oscillating with rate of $5\text{oscillations/min}$. By what percentage, should the magnetic field of earth be changed, so that the number of oscillations become $4\text{oscillations/min}$?

1. Increased by $72\%$
2. Decreased by $72\%$
3. Increased by $36\%$
4. Decreased by $36\%$

Q. Maximum magnetic field is found at a distance $x$ from the centre along the axis of circular loop $($radius $=R)$ of the current carrying conductor. What is the value of $x?$

1. $\frac{R}{2}$
2. Zero
3. $R$
4. $\frac{R}{\sqrt{2}}$

Q.

The mutual inductance between two planar concentric rings of radii $r_{1}and{r}_2(with{r}_1>>r_2)$ placed in air is given by

1. $\frac{{\mu }_0\pi r_2^2}{2r_1}$

2. $\frac{{\mu }_0\pi (r_1+r_2{)}^2}{2r_1}$

3. $\frac{{\mu }_0\pi (r_1+r_2{)}^2}{2r_2}$

4. $\frac{{\mu }_0\pi r_1^2}{2r_2}$

Q. What will be the Mutual Inductance if two coils are perpendicular and away from each other ?

Q. Define the term 'mutual inductance' between two coils.

Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii $r_1$ and $r_2(r_2>>r_1)$. Total number of turns in the two solenoids are $N_1$ and $N_2$ respectively.

Q. A magnet of magnetic moment $M$ oscillating freely in earth's horizontal magnetic field makes $n$ oscillations per minute. If the magetic moment is quadrupled and the earth's field is doubled, the numbers of oscillations made per minute would be:

1. $\frac{n}{2\sqrt{2}}$
2. $\frac{n}{\sqrt{2}}$
3. $2\sqrt{2}n$
4. $\sqrt{2n}$

Q.

A circular loop of radius 0.0157 m carries a current of 2.0 amp .The magnetic field at the center of the loop is

Q. The core of a toroid having $3000$ turns has inner and outer radial $11\text{cm}$ and $12\text{cm}$ respectively. The magnetic field in the core for a current of $0.7\text{A}$ is $2.5\text{T}$. Calculate the relative permeability of the core ?

1. $684$
2. $290$
3. $395$
4. $768$

Q. The current density in a wire of radius $‘a^{\prime }$ varies with radial distance $‘r^{\prime }$ as $J=k{r}^2$ , where $k$ is a constant .

1. The total current passing through the cross section of the wire is $I=\frac{\pi k{a}^4}{2}$
2. The total current passing through the cross section of the wire is $I=\frac{3\pi k{a}^4}{2}$
3. The magnetic field at a distance $r>a$ is $B=\frac{{\mu }_{0}k{a}^4}{4r}$
4. The magnetic field at a distance $r<a$ is $B=\frac{{\mu }_{0}k{r}^3}{4}$

Q. The current density $J$ inside a long, solid, cylindrical wire of radius $a=12\text{mm}$ is in the direction of the central axis, and its magnitude varies lenearly with radial distance $r$ from the axis according to $J=\frac{J_{0}r}{a}$ where $J_0=\frac{{10}^5}{4pi}{\text{A/m}}^2$ .Find the magnitude of the magnetic field at $r=\frac{a}{2}$ in $\mu \text{T}$.

Q.

The inner and outer coils of the two long co-axial solenoids are the same length and have radii of ${\mathrm{r}}_1\mathrm{and}{\mathrm{r}}_2$, as well as different numbers of turns per unit length, ${\mathrm{n}}_1\mathrm{and}{\mathrm{n}}_2$, respectively. The inner-self-inductance coils and mutual inductance are compared as follows:

1. $\begin{array}{l}\frac{n_2}{n_1}:\frac{r_2^2}{r_1^2}\end{array}$

2. $\begin{array}{l}\frac{n_2}{n_1}:\frac{r_1}{r_2}\end{array}$

3. $\begin{array}{l}\frac{n_1}{n_2}\end{array}$

4. $\begin{array}{l}\frac{n_2}{n_1}\end{array}$

Q. A long solid cylindrical conductor of radius $10\text{cm}$ carries a current of $4\text{A}$ which is uniformly distributed over its circular cross-section. The magnetic field at a distance of $5\text{cm}$ from the axis of the conductor is

1. $4\times {10}^{-6}\text{T}$
2. $2\times {10}^{-8}\text{T}$
3. $0.8\times {10}^{-7}\text{T}$
4. $0.4\times {10}^{-8}\text{T}$

Q.

The magnet of vibration magnetometer is heated so as to reduce its magnetic moment by $36\%$. By doing this the periodic time of the magnetometer will

1. Decreases by $64\%$

2. Increases by $36\%$

3. Decreases by $25\%$

4. Increases by $25\%$

Q. A long wire is bent into the shape shown in figure without cross contact at $\text{P}$. The radius of the circular section is $R.$ If current $I$ flows in the wire, then the magnetic field at the center $\text{C}$ is-

1. $\frac{{\mu }_{0}I}{2R}(1+\frac{1}{\pi })⨀$
2. $\frac{{\mu }_{0}I}{2R}(1+\frac{1}{\pi })⨂$
3. $\frac{{\mu }_{0}I}{2R}(1-\frac{1}{\pi })⨀$
4. $\frac{{\mu }_{0}I}{2R}(1-\frac{1}{\pi })⨂$

Q. At a place, the earth's horizontal component of magnetic field is $0.36\times {10}^{-4}{\text{weber/m}}^2$. If the angle of dip at that place is ${45}^{\circ }$, then the vertical component of earth's magnetic field at that place in $\mu \text{T}$ will be

Q. A straight wire is bent in a shape shown in the diagram. It carries a steady current $I$. The magnetic field at the Center $O$ of the arcs will be,

1. $\frac{{\mu }_{o}I}{4}\left(\frac{r_1}{r_2^2}\right)\otimes$
2. $\frac{{\mu }_{o}I}{4}\left(\frac{1}{r_2}\right)\odot$
3. $\frac{{\mu }_{o}I}{4}\left(\frac{r_1+r_2}{r_1{r}_2}\right)\otimes$
4. $\frac{{\mu }_{o}I}{4}\left(\frac{r_1+r_2}{r_1{r}_2}\right)\odot$

Q. Figure shows a square loop $\text{ABCD}$ with edge length $a$. The resistance of the wire $\text{ABC}$ is $r$ and that of $\text{ADC}$ is $2r$. The value of magnetic field at the center of the loop, assuming uniform wire is

1. $\frac{\sqrt{2}{\mu }_{0}i}{3\pi a}\odot$
2. $\frac{\sqrt{2}{\mu }_{0}i}{3\pi a}\otimes$
3. $\frac{\sqrt{2}{\mu }_{0}i}{\pi a}\odot$
4. $\frac{\sqrt{2}{\mu }_{0}i}{\pi a}\otimes$

Q. The frequency of oscillation of a bar magnet in an oscillation magnetometer in the earth's magnetic field is $40$ oscillations per $\text{minute}$. A short bar magnet is placed to the north of the magnetometer, at a separation of $20\text{cm}$ from the oscillating magnet, with its north pole pointing towards north as shown in figure. The frequency of oscillation is found to be increases to $60$ oscillations per $\text{minute}$. Calculate the magnetic moment of this short bar magnet.
[Horizontal component of the earth's magnetic field is $24\mu \text{T}$]

1. $1.2{\text{Am}}^2$
2. $12{\text{Am}}^2$
3. $0.12{\text{Am}}^2$
4. $120{\text{Am}}^2$

Q. Curves in the graph shown give, as functions of radial distance $r$, the magnitude $B$ of the magnetic field inside and outside for long wires $a,b,c$ and $d$, carrying currents that are uniformly distributed across the cross-sections of the wires. The wires are far from one another. The current density in wire $a$ is

1. greater than in wire $c$
2. less than in wire $b$
3. equal to that in wire $d$
4. less than in wire $d$

Q. The frequency of oscillation of a bar magnet in an oscillation magnetometer in the earth's magnetic field is $40$ oscillations per $\text{minute}$. A short bar magnet is placed to the north of the magnetometer, at a separation of $20\text{cm}$ from the oscillating magnet, with its north pole pointing towards north as shown in figure. The frequency of oscillation is found to be increases to $60$ oscillations per $\text{minute}$. Calculate the magnetic moment of this short bar magnet.
[Horizontal component of the earth's magnetic field is $24\mu \text{T}$]

1. $12{\text{Am}}^2$
2. $120{\text{Am}}^2$
3. $1.2{\text{Am}}^2$
4. $0.12{\text{Am}}^2$

Q.

What is Henry?