# Coupling

## Trending Questions

**Q.**

A vibration magnetometer placed in a magnetic meridian has a small bar magnet. The magnet executes oscillations with a time period of $2\mathrm{sec}$ 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

$1\mathrm{s}$

$2\mathrm{s}$

$3\mathrm{s}$

$4\mathrm{s}$

**Q.**A hollow cylindrical wire carries a current I, having inner and outer radii R and 2R respectively. Magnetic field at a point which 3R2 distance away from its axis is

- 5μ0I18πR
- μ0I36πR
- 5μ0I36πR
- 5μ0I9πR

**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 L1and L2 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

- M = L
_{1}/ L_{2} - M = L
_{1}L_{2} - M = √L
_{1}L_{2} - M = (L
_{1}L_{2})^{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 a3 and 2a, respectively from the axis of the wire, is:

- 23
- 2
- 12
- 32

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

- 1.6π μV
- 3.2π μV
- 4.8π μV
- 0.8π μV

**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

- 3
- 13
- √3
- 1√3

**Q.**An infinitely long hollow conducting cylinder with inner radius R2 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

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

- 1.0×10−5 T
- 1.0×10−7 T
- 1.5×10−7 T
- 1.5×10−5 T

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

- Increased by 72%
- Decreased by 72%
- Increased by 36%
- 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?

- R2
- Zero
- R
- R√2

**Q.**

The mutual inductance between two planar concentric rings of radii r1 and r2 (with r1>>r2) placed in air is given by

μ0πr222r1

μ0π(r1+r2)22r1

μ0π(r1+r2)22r2

μ0πr212r2

**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 r1 and r2(r2>>r1). Total number of turns in the two solenoids are N1 and N2 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:

- n2√2
- n√2
- 2√2 n
- √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 cm and 12 cm respectively. The magnetic field in the core for a current of 0.7 A is 2.5 T. Calculate the relative permeability of the core ?

- 684
- 290
- 395
- 768

**Q.**The current density in a wire of radius ‘a′ varies with radial distance ‘r′ as J=kr2 , where k is a constant .

- The total current passing through the cross section of the wire is I=πka42
- The total current passing through the cross section of the wire is I=3πka42
- The magnetic field at a distance r>a is B=μ0ka44r
- The magnetic field at a distance r<a is B=μ0kr34

**Q.**The current density J inside a long, solid, cylindrical wire of radius a=12 mm is in the direction of the central axis, and its magnitude varies lenearly with radial distance r from the axis according to J=J0ra where J0=1054 pi A/m2 .Find the magnitude of the magnetic field at r=a2 in μT.

**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:

$\begin{array}{l}\frac{{n}_{2}}{{n}_{1}}:\frac{{r}_{2}^{2}}{{r}_{1}^{2}}\end{array}$

$\begin{array}{l}\frac{{n}_{2}}{{n}_{1}}:\frac{{r}_{1}}{{r}_{2}}\end{array}$

$\begin{array}{l}\frac{{n}_{1}}{{n}_{2}}\end{array}$

$\begin{array}{l}\frac{{n}_{2}}{{n}_{1}}\end{array}$

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

- 4×10−6 T
- 2×10−8 T
- 0.8×10−7 T
- 0.4×10−8 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

Decreases by 64%

Increases by 36%

Decreases by 25%

Increases by 25%

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

- μ0I2R(1+1π) ⨀
- μ0I2R(1+1π) ⨂
- μ0I2R(1−1π) ⨀
- μ0I2R(1−1π) ⨂

**Q.**At a place, the earth's horizontal component of magnetic field is 0.36×10−4 weber/m2. If the angle of dip at that place is 45∘, then the vertical component of earth's magnetic field at that place in μT 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,

- μoI4(r1r22)⊗
- μoI4(1r2)⊙
- μoI4(r1+r2r1r2)⊗
- μoI4(r1+r2r1r2)⊙

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

- √2μ0i3πa⊙
- √2μ0i3πa⊗
- √2μ0iπa⊙
- √2μ0iπa⊗

**Q.**The frequency of oscillation of a bar magnet in an oscillation magnetometer in the earth's magnetic field is 40 oscillations per minute. A short bar magnet is placed to the north of the magnetometer, at a separation of 20 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 minute. Calculate the magnetic moment of this short bar magnet.

[Horizontal component of the earth's magnetic field is 24 μT]

- 1.2 Am2
- 12 Am2
- 0.12 Am2
- 120 Am2

**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

- greater than in wire c
- less than in wire b
- equal to that in wire d
- 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 minute. A short bar magnet is placed to the north of the magnetometer, at a separation of 20 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 minute. Calculate the magnetic moment of this short bar magnet.

[Horizontal component of the earth's magnetic field is 24 μT]

- 12 Am2
- 120 Am2
- 1.2 Am2
- 0.12 Am2

**Q.**

What is Henry?