IISER Physics - Magnetostatics
Exam Duration: 45 Mins Total Questions : 30
By magnetic screening we mean to cut out magnetic fields a small region. The material used for this purpose should be
- (a)
ferromagnetic
- (b)
antiferromagnetic
- (c)
paramagnetic
- (d)
diamagnetic
Neel temperature is a temperature
- (a)
below which antiferromagnetism occurs
- (b)
above which the substance is paramagnetic
- (c)
at which there is no net resultant magnetic moment in the absence of an applied magnetic field
- (d)
All of the above statements are correct
Angle of dip is maximum at
- (a)
poles
- (b)
equator
- (c)
latitude 45°
- (d)
latitude 60°
Angle of dip is maximum at poles. Its value is 900.
A magnetic dipole in the shape of a sphere placed in a uniform magnetic field of induction \(\overrightarrow { B } \) will, in general
- (a)
be displaced in the direction \(\overrightarrow { B } \)
- (b)
be displaced opposite to the direction of \(\overrightarrow { B } \)
- (c)
remain in equilibrium position after displacement from its initial position
- (d)
execute simple harmonic motion provided the amplitude of motion is small
When a dip circle is placed in the magnetic meridiam, the needle will make with the horizontal.
- (a)
an angle less than the dip at that place
- (b)
an angle greater than the dip at that place
- (c)
an angle equal to the dip at that place
- (d)
an angle equal to zero degree
Cosmic ray particles from outer space enter the earth's atmosphere. On entering the earth's magnetic field, the negatively charged particles in the cosmic rays will get deflected towards
- (a)
North
- (b)
South
- (c)
East
- (d)
West
Cosmic rays consist of high energy charged and uncharged particles that fall vertically on the earth 's surface from counter space, charged particles are influenced by the earth's Magnetic field.
In a dip circle the plane of oscillation of the needle is adjusted in such a way that it lies
- (a)
perpendicular to the magnetic meridian
- (b)
in the magnetic meridian
- (c)
45° to the magnetic meridian
- (d)
parallel to the magnetic moment
A magnet gave two null points located on its axis under the influence of the earth's field. In such a case the magnet must have been kept with its axis
- (a)
perpendicular to the meridian North Pole facing North
- (b)
perpendicular to the meridian South Pole facing North
- (c)
in the magnetic meridian South Pole facing North
- (d)
in the magnetic meridian North Pole facing North
A metal ball with a mass of 100 g is swung with an angular speed of \(40\pi \quad rad/s\) in a horizontal circle at the end of a taut string in the presence of a uniform vertical magnetic field of 100 G. The amount of positive charge q that must be placed on the ball to double the tension in the string is
- (a)
326 C
- (b)
1260 C
- (c)
630 C
- (d)
3780 C
Centripetal force = tension in the string
=Lorentz force
\(\frac{mv^{2}}{r}=qvB\) which gives \(\frac{mv}{r}=qB\)
Put \(v=r\omega\)
\(m\omega=qB\)
\(q=\frac{m\omega}{B}\)
Given m=100g=0.1 kg, ω=40π rad s-1,
B=100 G = 100x10-4
B = 10-2 T [Formula is 1 T=104 G]
q=\(\frac{0.1\times40 \pi}{10^{-2}}=400 \pi\)=1260 C
Ferromagnetism is
- (a)
maximum at 0ºC
- (b)
maximum at 0 K
- (c)
zero at 0 K
- (d)
minimum at 0 K but not zero
The ferromagnetism is maximum at 0Kand decreases with increasing temperature until it becomes zero at a characteristic critical temperature called the Curie temperature of the material. For higher temperature the sample is paramagnetic.
Hysteresis occurs in
- (a)
ferromagnetic material
- (b)
dielectric material
- (c)
elastic material
- (d)
ALL OF THE ABOVE
The term hysteresis is used generally to describe a system whose state depends on its previous history. When a ferromagnetic material is magnetised, the corresponding values of H and B trace out a closed curve called a hysteresis loop. Hysteresis also occurs in dielectric and elastic materials.
The magnetic compass is not useful for navigation near the magnetic poles.Since
- (a)
R =0
- (b)
V =0
- (c)
H =0
- (d)
\(\theta \) =0º
Magnetic does not work because near the magnetic poles, H=O.
Two bar magnets when placed with their similar poles together make 20 vib per min. When one of them is reversed the number of vibrations become 15 vib. per min. What is the ratio of their dipole moments?
- (a)
7:25
- (b)
25:7
- (c)
1:4
- (d)
4:1
M's are magnetic dipole moments. T's are time periods.
\(\frac{M_1}{M_2}=\frac{T_{2}^{2}+T_{1}^{2}}{T_{2}^{2}-T_{1}^{2}}=\frac{n_{1}^{2}+n_{2}^{2}}{n_{1}^{2}-n_{2}^{2}}=\frac{20^{2}+15^{2}}{20^{2}+15^{2}}\)
=\(\frac{400+225}{400-225}=\frac{625}{175}=\frac{25}{7}\)
A circular coil of 100 turns has an effective radius of 0.05 and current of 0.1A. How much work is done to turn it through 180° in a uniform field of 1.5W/m2 if the plane of the coil is initially perpendicular to the magnetic field?
- (a)
0.5523 J
- (b)
0.3255 J
- (c)
0.2355 J
- (d)
0.5235 J
\(W=mB(cos \theta_1 - cos \theta_2)\)
=mB(\(cos 0^{0}-cos180^{0}\))=2mB
=2(NiA)B
=2[100x0.1xπx(0.05)2]x1.5=0.2355 J
A magnet is suspended in a vertical plane which makes an angle of 30º with the magnetic meridian. In equilibrium, the axis of the magnet makes an angle of 45º with horizontal. What is the real value of dip at the place?
- (a)
4º
- (b)
40.9º
- (c)
45º
- (d)
NONE OF THESE
\(tan \delta=\frac{V}{H}\) and \(tan 45^{0}=\frac{V}{H cos 30^{0}}\)
\(\frac{tan \delta}{tan 45^{0}}=cos 30^{0}\)
\(tan \delta=cos 3^{0}=0.8660\)
\(\delta= tan ^{-1} (0.8660)=40.9^{0}\)
A vibration magnetometer consists of two identical bar magnets placed one over the other, such that they are mutually perpendicular and bisect each other. The time period of combination is 4 second. If one of the magnets is removed, find the period of other?
- (a)
5s
- (b)
3.36 s
- (c)
4.36 s
- (d)
5.36 s
Magnets placed perpenticular to eac have resultant magnetic moment = \(\sqrt{M^{2}+M^{2}}=\sqrt{2}M\)
\(T_1=2\pi \sqrt{\frac{2I}{\sqrt{2}MH}} \Rightarrow \frac{T_2}{T_1}=\frac{1}{(2)^{\frac{1}{4}}}\)
In the second case. T2=\(2\pi \sqrt{\frac{I}{MH}}\)
\(T_2=\frac{4}{(2)^{\frac{1}{4}}}=3.36s\)
A magnet oscillates in the earth's field with a time period T. It its mass is quadrupled, then its new time period will be
- (a)
4T
- (b)
2T
- (c)
T/2
- (d)
unaffected but motion is not SHM
\(T=2\pi \sqrt{\frac{I}{MH}}\)
\(T \propto \sqrt{I}\)
I \(\propto\) mass
T \(\propto\) \(\sqrt{Mass}\)
\(\frac{T_2}{T_1}=\sqrt{\frac{m_2}{m_1}}=\sqrt{\frac{4m_1}{m_1}}=2\)
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 \(700ºC\), then
- (a)
the time period increases
- (b)
the time period decreases
- (c)
the time period remains unchanged
- (d)
the needle stops vibrating
\(T=2\pi \sqrt{\frac{I}{MH}}\)
If temperature is more than Curie temperature the magnetic needle is demagnetized and then M reduces to zero, where M is Magnetic Moment of the oscillating magnet. H is horizontal component of the earth's magnetic field and I is 11101nent of inertia of the oscillating magnet. At temperature above Curie's temperature.
M=0, T=∞ so needle stops oscillating. Curie temperature tor iron is 7700C.
Unit of magnetic moment is
- (a)
Am-2
- (b)
NA-1m-1
- (c)
Nm
- (d)
Am2
To shield an instrument from the external magnetic field, it is placed inside a cabin made from
- (a)
wood
- (b)
ebonite
- (c)
iron
- (d)
diamagnetic substance
Reason: Iron has large permeability.
The vertical component of the earth's magnetic field is zero at a place where the angle of dip is
- (a)
\(0º\)
- (b)
45º
- (c)
60º
- (d)
90º
Which of the following substances has negative permeability and very large value of susceptibility?
- (a)
Ferromagnetic
- (b)
Paramagnetic
- (c)
Diamagnetic
- (d)
NONE OF THE ABOVE
A dip circle is so set that its needle moves freely in the magnetic meridian. In this position, the angle of dip is \(40º\). Now the dip circle is rotated so that the plane in which the needle moves makes an angle of \(30º\) with the magnetic meridian. In this position, the needle will dip by an angle
- (a)
\(40º\)
- (b)
\(30º\)
- (c)
more than \(40º\)
- (d)
less than \(40º\)
\(cot \delta=\sqrt{cot^{2}\delta_1+cot^{2}\delta_2}=\sqrt{cot^{2}40^{0}+cot^{2}30^{0}}\)
\(=\sqrt{{1.19^{2}}+3}=2.1\)
\(delta=25^{0}\)
Hence \(\delta<40^{0}\)
At a neutral point
- (a)
field of magnet is zero
- (b)
field of the earth is zero
- (c)
field of magnet is perpendicular to field of the earth
- (d)
NONE OF THE ABOVE
At neutral point. field due to Magnet is cancelled by field due to the earth.
A circular loop of radius 0.0157 m carries a current of 2.0 A. The magnetic field at the centre of the loop is \(\left[ { \mu }_{ 0 }=4\pi \times { 10 }^{ -7 }\quad weber/amp-m \right] \)
- (a)
\(1.57\times { 10 }^{ -5 }weber/{ m }^{ 2 }\)
- (b)
\(8.0\times { 10 }^{ -5 }weber/{ m }^{ 2 }\)
- (c)
\(2.0\times { 10 }^{ -5 }weber/{ m }^{ 2 }\)
- (d)
\(3.14\times { 10 }^{ -5 }weber/{ m }^{ 2 }\)
\(B=\frac{\mu_0I}{2r}\)
Put r=0.0157 m, I=2A
\(B=\frac{(4\pi \times10^{-7})^{2}}{2(0.0157)}=8\times10^{-5}\) Wb m-2
Two identical magnetic dipoles of magnetic moments 1.0 Am2 each, placed at a separation of 2 m with their axes perpendicular to each other. The resultant magnetic field at a point midway between the dipole is
- (a)
\(5\times { 10 }^{ -7 }T\)
- (b)
\(\sqrt { 5 } \times { 10 }^{ -7 }T\)
- (c)
\({ 10 }^{ -7 }T\)
- (d)
\(2\times { 10 }^{ -7 }T\)
Axes of the two dipoles are perpenticular to each other. The mid-point lies on axial line of one magnet and on equatorial line of other magnet.
\(B_1=\frac{\mu_0}{4\pi}.\frac{2M}{d^{3}}=\frac{10^{-7}\times2\times1}{1^{3}}=2\times10^{-7}T\)
\(B_2=\frac{\mu_0}{4\pi}.\frac{M}{d^{3}}=10^{-7}T\)
\(B_1 \bot B_2\) .Therefore resultant field = \(\sqrt{B_{1}^{2}+B_{2}^{2}}\) =\(\sqrt{5}\times10^{7}T\)
If a diamagnetic solution is poured into a U-tube and one arm of this U-tube is placed between the poles of a strong magnet, with the meniscus in line with the field, then the level of solution will
- (a)
rise
- (b)
fall
- (c)
oscillate slowly
- (d)
remain as such
Diamagnetic liquid moves from region of stronger parts of magnetic field to weaker parts.
A ferromagnetic material is heated above its Curie temperature. Which one is a correct statement?
- (a)
Ferromagnetic domains are perfectly arranged
- (b)
Ferromagnetic domains become random
- (c)
Ferromagnetic material changes into diamagnetic material
- (d)
Ferromagnetic domains are not affected
A vibration magnetometer is placed at the south pole, then the time period will be
- (a)
zero
- (b)
infinity
- (c)
same as at equator
- (d)
same as at any other place on the earth
T=\(2\pi \sqrt{\frac{I}{MH}}\)
At south pole, H=0, T=∞
Imaginary lines joining points of equal declination are called
- (a)
isoclinic
- (b)
Isogonic
- (c)
isodynamic
- (d)
NONE OF THESE