Master Resource Book in JEE Main Physics

D. B. Singh

Chapter 20

Magnetostatics - all with Video Answers

Educators

Section 1

Round 1

Problem 1

A magnet of magnetic moment $\mu$ and pole strength $m$ is divided in two equal parts, the magnetic moment of each part will be
(a) $M$
(b) $M / 2$
(c) $M / 4$
(d) $2 M$

Hunza Gilgit

Hunza Gilgit

Numerade Educator

Problem 2

The magnetie potential due to a magnetic dipole at a point on its axis distant $40 \mathrm{~cm}$ from its centre is found to be $2.4 \times 10^{-5} \mathrm{JA}^{-1} \mathrm{~m}^{-1}$. The magnetic moment of the dipole will be
(a) $28.6 \mathrm{Am}^{2}$
(b) $32.2 \mathrm{Am}^{2}$
(c) $38.4 \mathrm{Am}^{2}$
(d) None of these

Narayan Hari

Numerade Educator

Problem 3

A magnetie needle lying parallel to a magnetic field required $W$ units of work to turn it through $60^{\circ} .$ The torque required to maintain the needle in this position will be
(a) $\sqrt{3} w$
(b) $W$
(c) $\sqrt{3} \frac{W}{2}$
(d) $2 \mathrm{~W}$

Narayan Hari

Numerade Educator

Problem 4

A bar magnet of length $3 \mathrm{~cm}$ has a point $A$ and $B$ along axis at a distance of $24 \mathrm{~cm}$ and $48 \mathrm{~cm}$ on the opposite ends. Ratio of magnetic fields at these points will be
(a) 8
(b) 3
[c) 4
idi $1 / 2 \sqrt{2}$

Narayan Hari

Numerade Educator

Problem 5

Rate of change of torque $\tau$ with deflection $q$ is maximum for a magnet suspended freely in a uniform magnetic field of induction $B$, when
(a) $\theta=0^{-}$
(b) $\theta=45$ "
(c) $\theta=60^{-}$
(d) $\theta=90^{-}$

Narayan Hari

Numerade Educator

Problem 6

Two short bar magnets with magnetic moments 400 ab-amp $\mathrm{cm}^{2}$ and 800 ab-amp $\mathrm{cm}^{2}$ are placed with their axis in the same straight line with similar poles facing each other and with their centres at $20 \mathrm{~cm}$ from each other. Then the force of repulsion is
(a) 12 dyne
(b) 6 dyne
(c) 800 dyne
(d) 150 dyne

Narayan Hari

Numerade Educator

Problem 7

Two magnets have the same length and the same pole strength. But one of the magnets has a small hole at its centre. Then
(a) both the equal magnetic moment
(b) one with hale has smaller magnetic moment
(c) one with hole has large magnetic moment
(d) one with hole loses magnetism through the hole

Narayan Hari

Numerade Educator

Problem 8

Two magnets of equal magnetic moments $M$ each are placed as shown in figure. The resultant magnetic moment is
(a) $M$
(b) $\sqrt{3} \mathrm{M}$
(c) $\sqrt{2} \mathrm{M}$
(d) $M / 2$

Narayan Hari

Numerade Educator

Problem 9

A short bar magnet placed with its axis at $30^{\circ}$ with a uniform external magnetic field of $0.25 \mathrm{~T}$ experiences a torque of magnitude equal to $4.5 \times 10^{-2} \mathrm{~J}$, then the magnitude of magnetic moment of the magnet is? [NCERT]
(a) $0.36 \mathrm{~J} / \mathrm{T}$
(b) $3.6 \mathrm{~J} / \mathrm{T}$
(c) $8.6 \mathrm{JT}$
(d) $0.86 \mathrm{~J} / \mathrm{T}$

Narayan Hari

Numerade Educator

Problem 10

In which orientation the resultant magnetic moment of two magnets, will be zero, if magnetic moment of each magnets is $M$ in the following flgures?
(b]
(a)
(c)
[d]

Narayan Hari

Numerade Educator

Problem 11

A closely wound solenoid of 800 turns and area of cross-section $2.5 \times 10^{-4} \mathrm{~m}^{2}$ earries a current of $3.0 \mathrm{~A}$. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?
(a) $6 \underline{J}]{T}$
(b) $0.9 \mathrm{~J} / \mathrm{T}$
(c) $9 \mathrm{~J} / \mathrm{T}$
(d) $0.6 \mathrm{~J} / \mathrm{T}$

Narayan Hari

Numerade Educator

Problem 12

A bar magnet is cut into two equal halves by a plane parallel to the magnetic axis. Of the following physical quantities, the one which remains unchanged is.
(a) pole strength
(b) magnetic moment
(c) intensity of magnetisation
(d) moment of inertia

Narayan Hari

Numerade Educator

Problem 13

A toroid of $n$ turns, mean radius $R$ and cross-sectional radius a carries current $I$. It is placed on a horizontal table taken as $x-y$ plane. Its magnetic moment $\mathbf{m} \quad$ [NCERT Exemplar]
(a) is non-zero and points in the z-direction by symmetry
(b) points along the axis of the toroid $(\mathrm{m}=\mathrm{m}$ ) (c) is zero, otherwise there would be a field falling as $\frac{1}{r^{3}}$ at large distances outside the toroid
(d) is pointing radially outwards

Hunza Gilgit

Numerade Educator

Problem 14

The vertical component of earth's magnetic field is zero at or the earth's magnetic field always has a vertical component except at the INCERT Exemplar]
[a) Magnetic poles
(b) Geographic poles
(c) Every place
(d) Magnetic equator

Narayan Hari

Numerade Educator

Problem 15

The earth's magnetic field at a certain place has a horizontal component of $0.3 \mathrm{G}$ and total strength $0.5 \mathrm{G}$. Find angle of dip in $\tan ^{-1}$.
(a) $\delta=\tan ^{-1} \frac{4}{3}$
(b) $\delta=\tan ^{-1} \frac{3}{4}$
(c) $\vec{b}=\tan ^{-1} \frac{5}{3}$
(d) $\delta=\tan ^{-1} \frac{3}{5}$

Narayan Hari

Numerade Educator

Problem 16

A short bar magnet with the north pole facing north forms a neutral point a $P$ in the horizontal plane. If the magnet is rotated by $90^{\circ}$ in the horizontal plane, the net magnetie induetion at $P$ is (Horizontal component of earth's magnetic field $=B_{H}$ )
(a) zero
(b) $2 B_{H}$
(c) $\frac{\sqrt{5}}{2} B_{H}$
(d) $\sqrt{5} B_{H}$

Hunza Gilgit

Numerade Educator

Problem 17

The earth's magnetic induction at a certain point is $7 \times 10^{-5} \mathrm{Wbm}^{-2}$. This is to be annulled by the magnetic induction at the centre of a circular conducting loop of radius $15 \mathrm{~cm}$. The required current in the loop is
(a) $0.56 \mathrm{~A}$
(b) $5.6 \mathrm{~A}$
(c) $0.28 \mathrm{~A}$
(d) $2.8 \mathrm{~A}$

Narayan Hari

Numerade Educator

Problem 18

A bar magnet is placed north-south with its north pole due north. The points of zero magnetic field will be in which direction from centre of magnet
(a) north and south
(b) east and west
(c) north-east and south-west
(d) north-east and south-east

Narayan Hari

Numerade Educator

Problem 19

The magnetic field of the earth can be modelled by that of a point dipole placed at the centre of the earth. The dipole axis makes an angle of $11,3^{\circ}$ with the axis of the earth. At Mumbai, declination is nearly zero.Then. INCFRT Exemplar]
(a) the declination varies between $11.3^{*} \mathrm{~W}$ to $11,3^{-} \mathrm{E}$
(b) the least declination is $0^{*}$
(c) the plane defined by dipole axis and Earth axis passes through Grecmwich
(d) declination averaged over Earth must be always negative

Hunza Gilgit

Numerade Educator

Problem 20

A magnet is placed on a paper in a horizontal plane for locating neutral points. A dip needle placed at the neutral point will be horizontal at the
(a) magnetic poles
(b) magnetic equator
(c) latitude angle $45^{\circ}$
(d) latitude angle of $60^{*}$

Narayan Hari

Numerade Educator

Problem 21

A bar magnet $20 \mathrm{~cm}$ in length is placed with its south pole towards geographie north. 'The neutral points are situated at a distance of $40 \mathrm{~cm}$ from centre of the magnet. If horizontal component of earth's field $3.2 \times 10^{-5} \mathrm{~T}$, then pole strength of magnet is
(a) $5 \mathrm{Am}$
(b) $10 \mathrm{Am}$
(c) $45 \mathrm{Am}$
(d) 20 Am

Narayan Hari

Numerade Educator

Problem 22

In a permanent magnet at room temperature [NCERT Exemplar]
(a) magnetic moment of each molecule is zero
(b) the individual molecules have non-zero magnetic moment which are all perfectly aligned
(c) domains are partially aligned
(d) domains are all perfectly aligned

Narayan Hari

Numerade Educator

Problem 23

At a certain place, the horizontal component of the earth's magnetic field is $B_{0}$ and the angle of dip is $45^{\circ}$. The total intensity of the field at that place will be
(a) $B_{0}$
(b) $\sqrt{2} B_{0}$
(c) $2 B_{0}$
(d) $B_{0}^{1}$

Narayan Hari

Numerade Educator

Problem 24

Consider the two idealized systems: (i) a parallel plate capacitor with large plates and small separation and (ii) a long solenoid of length $L>R$, radius of cross-section. In (i) $E$ is ideally treated as a constant between plates and zero outside. In (ii) magnetic field is constant inside the solenoid and zero outside. These idealised assumptions, however, contradict fundamental laws as below [NCERT Exemplat]
(a) case (i) contradicts Gauss's law for electrostatic fields.
(b) case (i) contradicts Gauss's law for magnetic field.
(c) case (i) agrees with $\int \mathbb{E} d=0$.
(d) case (ii) contradicts $\int \mathrm{H} \cdot d \mathrm{l}=\mathrm{I}_{\mathrm{ea}}$

Hunza Gilgit

Numerade Educator

Problem 25

The variation of the intensity of magnetisation $(I)$ with respect to the magnetising field $(H)$ in a diamagnetic substance is described by the graph in figure.
(a) $O \bar{D}$
(b) $O C$
(c) $O B$
(d) $O A$

Narayan Hari

Numerade Educator

Problem 26

A rod of ferromagnetic material with dimensions $10 \mathrm{~cm} \times 0.5 \mathrm{~cm} \times 0.2 \mathrm{~cm}$ is placed in a
magnetic field of strength $0.5 \times 10^{4} \mathrm{~A}-\mathrm{m}^{-1}$ as a result of which a magnetic moment of $5 \mathrm{~A}-\mathrm{m}^{-2}$ is produced in the rod. The value of magnetic induetion will be
(a) $0.54 \mathrm{~T}$
(b) $6.28 \mathrm{~T}$
(c) $0.358 \mathrm{~T}$
(d) $2.591 \mathrm{~T}$

Narayan Hari

Numerade Educator

Problem 27

The space inside a toroid is filled with tungusten shoes susceptibility is $6.8 \times 10^{-5}$. The percentage increase in the magnetic field will be
(a) $0.0068 \%$
(b) $0.06806$
(c) $0.68 \%$
(d) None of these

Narayan Hari

Numerade Educator

Problem 28

The horizontal component of flux density of earth's magnetic field is $1.7 \times 10^{-5} \mathrm{~T}$. The value of horizontal component of intensity of earth's magnetic field will be
(a) $24.5 \mathrm{Am}^{-1}$
(b) $13.5 \mathrm{Am}^{-1}$
(c) $1.53 \mathrm{Am}^{-1}$
(d) $0.35 \mathrm{Am}^{-1}$

Narayan Hari

Numerade Educator

Problem 29

A loop of area $0.5 \mathrm{~m}^{2}$ is placed in a magnetic field of strength $2 \mathrm{~T}$ in direction making an angle of $30^{\circ}$ with the field. The magnetic flux linked with the loop will be
(a) $\frac{1}{2} W b$
(b) $\sqrt{\frac{3}{2}} \mathrm{~Wb}$
(c) $2 W \bar{b}$
(d) $\frac{\sqrt{3}}{2} \mathrm{~Wb}$

Narayan Hari

Numerade Educator

Problem 30

The time period of a thin bar magnet in earth's magnetic field is $T$. If the magnet is cut into four equal parts perpendicular to its length, the time period of each part in the same field will be
(a) $T / 2$
(b) $T / 4$
(c) $\sqrt{2}$
(d) $2 T$

Narayan Hari

Numerade Educator

Problem 31

A magnet freely suspended in a vibration magnetometer makes 40 oscillations per minute at a place $A$ and 20 oscillations per minute at a place $B$. If the horizontal component of earth's magnetic field at $A$ is $36 \times 10^{-6} \mathrm{~T}$, then its value at $B$ is
(a) $36 \times 10^{-6} \mathrm{~T}$
(b) $9 \times 10^{-6} \mathrm{~T}$
(c) $144 \times 10^{-6} \mathrm{~T}$
(d) $228 \times 10^{-6} \mathrm{~T}$

Narayan Hari

Numerade Educator

Problem 32

Two magnets held together in earth's magnetic field with same polarity together make 12 vib-min $^{-1}$ and when opposite poles together make 4 vib-min $^{-1}$. The ratio of magnetie moments is
(a) $9: 1$
(b) $1: 3$
(c) $1: 9$
(d) $5: 4$

Narayan Hari

Numerade Educator

Problem 33

A magnet performs 10 oscillations per minute in a horizontal plane at a place where the angle of dip is $45^{\circ}$ and the total intensity is $0.707$ CGS units. The number of oscillations per minute at a place where dip angle is $60^{\circ}$ and total intensity is $0.5$ CGS units will be
(a) 5
(b) 7
(c) 9
(d) 11

Narayan Hari

Numerade Educator

Problem 34

A circular coil of 16 turns and radius $10 \mathrm{~cm}$ carrying a current of $0.75$ A rests with its plane normal to an external field of magnitude $5.0 \times 10^{-2} \mathrm{~T} .$ The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a frequency of $2.0 / \mathrm{s}$. What is the moment of inertia of the coil about its axis of rotation?
(a) $1.2 \times 10^{-4} \mathrm{~g}-\mathrm{cm}^{2}$
(b) $3 \times 10^{-4} \mathrm{~kg}-\mathrm{m}^{2}$
(c) $0.3 \times 10^{-4} \mathrm{~kg}-\mathrm{m}^{2}$
(d) $1.2 \times 10^{-4} \mathrm{~kg}-\mathrm{m}^{2}$

Prem Bijarniya

Numerade Educator

Problem 35

At a certain place a magnet makes 30 oscillations per minute. At another place where the magnetic field is double, its time period will be
(a) $\sqrt{2} \mathrm{~s}$
(b) $2 \mathrm{~s}$
(c) 45
(d) $\frac{1}{2} s$

Narayan Hari

Numerade Educator

Problem 36

Two bar magnets having same geometry with magnetic moments $M$ and $2 M$ are firstly placed in such a way that their similar poles are same side. Time period of oscillations is $T_{1}$. Now the polarity of one of the magnets is reversed, and time period of oscillations is $T_{1}$. Now the polarity of one of the magnets is reversed and time period of oscillation is $T_{2}$
(a) $T_{1}<T_{1}$
(b) $T_{1}=T_{2}$
[c) $T_{1}>T_{2}$
(d) $T_{2}=\infty$

Narayan Hari

Numerade Educator

Problem 37

The magnetic needle of a tangent galvanometer is deflected at an angle $30^{\circ}$ due to a magnet. The horizontal component of earth's magnetic field $0.34 \times 10^{-4} \mathrm{~T}$ is along the plane of the coil. The magnetic intensity is
(a) $1.96 \times 10^{-4} \mathrm{~T}$
(b) $1.96 \times 10^{4} \mathrm{~T}$
(c) $1.96 \times 10^{-5} \mathrm{~T}$
(d) $1.96 \times 10^{5} \mathrm{~T}$

Narayan Hari

Numerade Educator

Problem 38

The period of oscillation of a freely suspended bar magnet is $4 s$. If it is cut into two equal parts in length, then the time period of each part will be
[a) $4 \mathrm{~s}$
(b) $2 \mathrm{~s}$
(c) $0.5 \mathrm{~s}$
(d) $0.25 \mathrm{~s}$

Hunza Gilgit

Numerade Educator

Problem 39

Two tangent galvanometers having coils of the same radius are connected in series. A current flowing in them produces deflections of $60^{\circ}$ and $45^{\circ}$ respectively. The ratio of the number of turns in the coils is
(a) $4 / 3$
(b) $(\sqrt{3}+1) / 1$
(c) $\frac{\sqrt{3}+1}{\sqrt{3}-1}$
(d) $\frac{\sqrt{3}}{1}$

Narayan Hari

Numerade Educator

Problem 40

A paramagnetic sample shows a net magnetisation of $8 \mathrm{Am}^{-1}$ when placed in an external magnetie field of $0.6 \mathrm{~T}$ at a temperature of $4 \mathrm{~K}$. When the same sample is placed in an external magnetic field of $0.2 \mathrm{~T}$ at a temperature of $16 \mathrm{~K}$, the magnetisation will be [NCFRT Exemplar]
(a) $\frac{32}{3} \mathrm{Am}^{-1}$
(b) $\frac{2}{3} \mathrm{Am}^{-1}$
(c) $6 \mathrm{Am}^{-1}$
(d) $2.4 \mathrm{Am}^{-1}$

Narayan Hari

Numerade Educator

Problem 41

A tangent galvanometer has a coil of 25 turns and a radius of $15 \mathrm{~cm}$. The horizontal component of the earth's magnetic field is $3 \times 10^{-5} \mathrm{~T}$. The current required to produce a deflection of $45^{\circ}$ in it is
(a) $0.29 \mathrm{~A}$
(b) $0.14 \mathrm{~A}$
(c) $1.2 \overline{\mathrm{A}}$
(d) $3.6 \times 10^{-5} \mathrm{~A}$

Narayan Hari

Numerade Educator

Problem 42

A bar magnet is oscillating in the Earth's magnetic field with a period $T$. What happens to its period of motion if its mass is quadrupled?
(a) Motion remains SHM with time period $=T / 2$
(b) Motion remains SHM and period remains nearly constant
(c) Motion temains SHM with time period $=2 T$
(d) Motion remains SHM with time period = $4 \mathrm{~T}$

Narayan Hari

Numerade Educator

Problem 43

A vibration magnetometer consists of two identical bar magnets placed one over the other such that they are perpendicular and bisect each other. The time period of oscillation in a horizontal magnetic field is $2^{5 / 4}$ s. One of the magnets is removed and if the other magnet oscillates in the same field, then the time period in second is
(a) $2^{1 / 4}$
(b) $2^{10}$
(c) 2
(d) 4

Narayan Hari

Numerade Educator

Problem 44

The time of vibration of a dip needle vibrating in the vertical plane is 3s. When magnetic needle is made to vibrate in the horizontal plane, the time of vibration is $3 \sqrt{2}$ s. Then the angle of dip is
(a) $30^{\circ}$
(b) $45^{\circ}$
(c) 60
(d) $90^{\circ}$

Narayan Hari

Numerade Educator

Problem 45

A compass needle placed at a distance $r$ from a short magnet in tan $A$ position shows a deflection of $60^{\circ} .$ If the distance is increased to $r(2)^{1 / 3}$, the deflection of compass needle is
(a) $30^{\circ}$
(b) $60^{\circ}$
(c) $45^{\circ}$
(d) $0^{\circ}$

Narayan Hari

Numerade Educator

Problem 46

The correct $I \cdot H$ curve for a paramagnetie material is represented by, figure.
(a)
(b)
(c)
(d)

Narayan Hari

Numerade Educator

Problem 47

A circular current loop of magnetic moment is in an arbitrary orientation in an external magnetic field $B$. The work done to rotate the loop by $30^{\circ}$ about an axis perpendicular to is planers [NCFRT Exemplar]
(a) $\mathrm{MB}$
(b) $\sqrt{3} \frac{M B}{2}$
(c) $\frac{M B}{2}$
(d) $\overrightarrow{0}$

Narayan Hari

Numerade Educator

Problem 48

Two bar magnets of the same mass, same length and breadth but having magnetic moments $M$ and $3 M$ are joined together pole and suspended by a string. The time period of assembly in a magnetic field of strength $H$ is 3 s. If now the polarity of one of the magnets is reversed and the combination is again made to oscillate in the same field, the time of oscillation is
(a) $3 \mathrm{~s}$
(b) $3 \sqrt{3} \mathrm{~s}$
(c) $3 / \sqrt{3} \mathrm{~s}$
(d) $6 \mathrm{~s}$

Narayan Hari

Numerade Educator

Problem 49

The variation of magnetic susceptibility $(\chi)$ with temperature for a diamagnetic substance is best represented by figure
(a)
(b]
(c)
(d)

Narayan Hari

Numerade Educator

Problem 50

A uniform magnetie field parallel to the plane of paper, exsisted 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 figure.
(a)
(b)
(c)
(d)

Narayan Hari

Numerade Educator

Problem 51

The variation of magnetic susceptibility $(\chi)$ with absolute temperature $T$ for a ferromagnetic is given in figure, by
(a)
(b)
(c)
(d)

Narayan Hari

Numerade Educator

Problem 52

A copper rod is suspended a non-homogeneous magnetic field region. The rod when in equilibrium will align itself
(a) in the region where magnetic ficld is strongest
(b) in the region where magnetic field is weakest and parallel to direction of magnetic field there
(c) in the direction in which it was originally suspended
(d) in the region where magnetic ficld is weakest and perpendicular to the direction of magnetic field there

Narayan Hari

Numerade Educator

Problem 53

The relative permeability of a substance $X$ is slightly less than unity and that of aubstance $Y$ is slightly more than unity, then
(a) $X$ is paramagnetic and $Y$ is ferromagnetic
(b) $X$ is diamagnetic and $Y$ is ferromagnetic
(c) $X$ and $Y$ both are paramagnetic
(d) $X$ is diamagnetic and $Y$ is paramagnetic

Narayan Hari

Numerade Educator

Problem 54

The magnetising field required to be applied in opposite direction to reduce residual magnetism to zero is called
(a) coercivity
(b) retentivity
[c) hysteresis
(d) None of the above

Narayan Hari

Numerade Educator

Problem 55

The hysteresis cycle for the material of a transformer core is
(a) short and wide
(b) tall and narrow
(c) tall and wide
[d) short and narrow

Narayan Hari

Numerade Educator