Magnetism & Matter - Live Session - 20 August 2020Contact Number: 9667591930 / 8527521718

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A bar magnet of length l and magnetic dipole moment M is bent to form an arc which subtends an angle of $120\xb0$ at centre. The new magnetic dipole moment will be

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

2. $\frac{3\sqrt{3}\mathrm{M}}{2\mathrm{\pi}}$

3. $\frac{3\mathrm{M}}{\mathrm{\pi}}$

4. $\frac{2\mathrm{M}}{\mathrm{\pi}}$

Two small bar magnets are placed in the air at a distance r apart. The magnetic force between them is proportional to:

(1) ${r}^{2}$

(2) ${r}^{-2}$

(3) ${r}^{-3}$

(4) ${r}^{-4}$

A short magnetic dipole is placed at the origin with its dipole movement directed along the +x-axis. If magnetic field induction at a point P (r, 0) is \(B\hat{i}\), the magnetic field induction at point Q (0, 2r) will be:

1. \(-\frac{B}{16}\hat{i}\)

2. \(-\frac{B}{8}\hat{j}\)

3. \(\frac{B}{16}\hat{j}\)

4. \(-\frac{B}{16}\hat{j}\)

The magnetic field at a point x on the axis of a small bar magnet is equal to the field at a point y on the equator of the same magnet. The ratio of the distances of x and y from the centre of the magnet is:

1. ${2}^{-3}$

2. ${2}^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

3. ${2}^{3}$

4. ${2}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

A sensitive magnetic instrument can be shielded very effectively from outside magnetic fields by placing it inside a box of

1. Teak wood

2. Plastic material

3. Soft iron of high permeability

4. A metal of high conductivity

A uniform magnetic field, parallel to the plane of the paper existed in space initially directed from left to right. When a bar of soft iron is placed in the field parallel to it, the lines of force passing through it will be represented by

1.

2.

3.

4.

Points A and B are situated perpendicular to the axis of a 2cm long bar magnet at large distances X and 3X from its centre on opposite sides. The ratio of the magnetic fields at A and B will be approximately equal to

(a) 1 : 9 (b) 2 : 9

(c) 27 : 1 (d) 9 : 1

Two short magnets with their axes horizontally perpendicular to the magnetic meridian are placed with their centres 40 *cm *east and 50 *cm* west of the magnetic needle. If the needle remains undeflected, the ratio of their magnetic moments is

(1) 4:5

(2) 16:25

(3) 64:125

(4) 2:$\sqrt{5}$

If a bar magnet of magnetic moment *M* is freely suspended in a uniform magnetic field of strength *B*, the work done in rotating the magnet through an angle is

1. $MB(1-\mathrm{sin}\theta )$

2. $MB\mathrm{sin}\theta $

3. $MB\mathrm{cos}\theta $

4. $MB(1-\mathrm{cos}\theta )$

Two small bar magnets are placed in a line with like poles facing each other at a certain distance *d* apart. If the length of each magnet is negligible as compared to *d*, the force between them will be inversely proportional to

1. d

2. d^{2}

3. $\frac{1}{{d}^{2}}$

4. ${d}^{4}$

A magnet of magnetic moment *M* is situated with its axis along the direction of a magnetic field of strength B. The work done in rotating it by an angle of 180^{o} will be

(1) -MB

(2) +MB

(3) 0

(4) +2MB

A long magnetic needle of length 2*L*, 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. $\frac{M}{2},\frac{m}{2}$

2. $M,\frac{m}{2}$

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

4. M, m

A bar magnet of magnetic moment 10^{4}*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 4×10^{–5} *T* to a direction 60° from the field will be

1. 0.2 *J* 2. 2.0 *J*

3. 4.18 *J* 4. 2 × 10^{2 }*J*

Two equal bar magnets are kept as shown in the figure. The direction of the resultant magnetic field, indicated by arrowhead at the point *P* is: (approximately)** **

1. | 2. | ||

3. | 4. |

A straight wire carrying a current *i *is turned into a circular loop. If the magnitude of the magnetic moment associated with it in M.K.S. unit is *M*, the length of wire will be

1. $4\mathrm{\pi iM}$ 2. $\sqrt{\frac{4\mathrm{\pi M}}{i}}$

3. $\sqrt{\frac{4\mathrm{\pi i}}{M}}$ 4. $\frac{M\mathrm{\pi}}{4i}$

Two similar bar magnets *P* and *Q*, each of magnetic moment *M*, are taken. If *P* is cut along its axial line and *Q* is cut along its equatorial line, all the four pieces obtained have:

1. | equal pole strength |

2. | magnetic moment M/4 |

3. | magnetic moment M/2 |

4. | magnetic moment M |

Two bar magnets with magnetic moments 2 *M* and *M* are fastened together at right angles to each other at their centres to form a crossed system, which can rotate freely about a vertical axis through the centre. The crossed system sets in earth’s magnetic field with magnet having magnetic moment 2*M* making an angle *$\theta $* with the magnetic meridian such that

(a) $\theta ={\mathrm{tan}}^{-1}\left(\frac{1}{\sqrt{3}}\right)$ (b) $\theta ={\mathrm{tan}}^{-1}\left(\sqrt{3}\right)$

(c) $\theta ={\mathrm{tan}}^{-1}\left(\frac{1}{2}\right)$ (d) $\theta ={\mathrm{tan}}^{-1}\left(\frac{3}{4}\right)$

A magnetic needle suspended by a silk thread is vibrating in the earth's magnetic field. If the temperature of the needle is increased by 500°*C*, then

(1) The time period decreases

(2) The time period remains unchanged

(3) The time period increases

(4) The needle stops vibrating

A superconductor exhibits perfect :

(1) Ferrimagnetism

(2) Ferromagnetism

(3) Paramagnetism

(4) Diamagnetism

Two short magnets of equal dipole moments *M* are fastened perpendicularly at their centres (figure). The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is :

1. $\frac{{\mu}_{0}}{4\mathrm{\pi}}\frac{M}{{d}^{3}}$

2. $\frac{{\mu}_{0}}{4\mathrm{\pi}}\frac{M\sqrt{2}}{{d}^{3}}$

3. $\frac{{\mu}_{0}}{4\mathrm{\pi}}\frac{2\sqrt{2}M}{{d}^{3}}$

4. $\frac{{\mu}_{0}}{4\mathrm{\pi}}\frac{2M}{{d}^{3}}$

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