Magnetism and Matter Test -14

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Magnetism and Matter Test -14

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Weekly Quiz Competition

Question 1
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Magnetic field intensity is defined as

A
Magnetic moment per unit volume

B
Magnetic induction force acting on a unit magnetic pole

C
Number of lines of force crossing per unit area

D
Number of lines of force crossing per unit volume

Solution

Number of lines of force passing through per unit area normally is intensity of magnetic field.
Question 2
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Assertion: We cannot think of magnetic field configuration with three poles.

Reason: A bar magnet does exert a torque on itself due to its own field.

(A) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(B) If both assertion and reason are true but reason is not the correct explanation of the assertion

(C) If assertion is true but reason is false.

(D) If the assertion and reason both are false.

A
A

B
B

C
C

D
D

Solution

It is quite clear that magnetic poles always exist in pairs. Since one can imagine magnetic field configuration with three poles.

When north poles or south poles of two magnets are glued together. They provide a three-pole field configuration. It is also known that a bar magnet does not exert a torque on itself due to own its field.
Question 3
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The susceptibility of paramagnetic substance is

A
Constant

B
Zero

C
Infinity

D
Depends on magnetic field

Solution

The susceptibility of paramagnetic substance is Constant.
Question 4
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A bar magnet of magnetic moment M is cut into two equal parts perpendicular to its length. The magnetic moment of either part is

A
M

B
M/2

C
2M

D
0

Solution

M = (length of magnet) x (pole strength).

When the magnet is cut into two equal parts, the length is halved or otherwise the pole strength becomes half.

In both cases magnetic moment. Becomes = M/2
Question 5
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S. I unit of pole strength is

A
N

B
N/A−m

C
A − m

D
T

Solution

SI unit of pole strength is ampere-meter and SI unit of magnetic moment is ampere meter²
Question 6
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A metallic rod of mass per unit length $$0.5$$ kg $$m^{-1}$$ is lying horizontally on a smooth inclined plane which makes an angle of $$30^o$$ with the horizontal. The rod is not allowed to slide down by a flowing a current through it when a magnetic field of induction $$0.25$$T is acting on it in the vertical direction. The current flowing in the rod to keep it stationary is?

A
$$14.76$$A

B
$$7.14$$A

C
$$11.32$$A

D
$$5.98$$A

Solution

$$B=0.25 T$$

$$\displaystyle\frac{m}{l}=0.5 \dfrac{kg}{m}$$

$$\theta =30^o$$

$$F=Bil$$

$$F\cos 30$$ balances $$mg \sin 30$$

$$\therefore (Bil) cos30^{o} =mg\sin 30$$

$$\Rightarrow i=\displaystyle\frac{m}{l}\frac{g}{B}\displaystyle\frac{\sin 30}{\cos 30}=\frac{0.5\times 9.8}{0.25\times 866}\times \frac{1}{2}=11.32A$$
Question 7
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Relation between magnetic moment and angular velocity is

A
$$M\propto \omega$$

B
$$M\propto \omega^{2}$$

C
$$M\propto \sqrt {\omega}$$

D
None of these

Solution

Magnetic moment,
$$M = Ia = l(\pi r^{2}) = \dfrac {q}{T}\times \pi r^{2} (\because q = lt)$$.
As, $$\omega = \dfrac {2\pi}{T}$$
$$\therefore M = \dfrac {q\omega r^{2}}{2}$$
$$\Rightarrow M \propto \omega$$
Question 8
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Which of the following is true regarding dimagnetic substances (symbols have their usual meaning)?

A
$${ \mu }_{ r }>1,{ \chi }_{ m }>1$$

B
$${ \mu }_{ r }>1,{ \chi }_{ m }<1$$

C
$${ \mu }_{ r }<1,{ \chi }_{ m }<0$$

D
$${ \mu }_{ r }<1,{ \chi }_{ m }>0$$

Solution

Diamagnetic substances induce magnetic field in the direction opposite to an external applied magnetic field and thus are repelled by external applied magnetic field.
Magnetic susceptibility of these substances is very small and negative i.e $$\chi_m < 0$$
For example:
For silicon, $$\chi_m = -4.2 \times 10^{-6}$$
From the equation, $$\mu_r = 1+ \chi_m$$
Thus, $$\chi_m<0$$ $$\implies \mu_r <1$$
Hence, such materials have magnetic permeability less than unity.
Question 9
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According to Lenz's law there is conversion of

A
Momentum

B
Collision

C
Voltage

D
Energy

Solution

Lenz's law deals with conversion of mechanical energy into electromagnetic energy in case of electromagnetic induction. Hence Lenz's law is basically a conversion of energy from one form to another.
Question 10
1 / -0

The magnetic moment $$(\mu)$$ of a revolvng electron around the nucleus varies with principle quantum number n as

A
$$\mu \propto n$$

B
$$\mu \propto 1/n$$

C
$$\mu \propto n^2$$

D
$$\mu \propto 1/n^2$$

Solution

Magnetic moment $${\mu}$$ of a revolving electron around the nucleus $$=n\mu_B$$
Where $$\mu_B=\displaystyle\frac{eh}{4\pi m}$$=Bohr Magneton.
So, $$\mu \propto n$$
Question 11
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The minimum magnetic dipole moment of electron in hydrogen atom is

A
$$\dfrac { eh }{ 2\pi m } $$

B
$$\dfrac { eh }{ 4\pi m } $$

C
$$\dfrac { eh }{ \pi m } $$

D
0

Solution

$$\displaystyle I=\dfrac { ev }{ 2\pi r } \\ \mu =IA=\dfrac { ev }{ 2\pi r } \times \pi { r }^{ 2 }=\dfrac { evr }{ 2 } =\dfrac { e }{ 2m } (mvr)\\ l=mvr=\dfrac { nh }{ 2\pi } \\ \mu =\dfrac { neh }{ 4\pi m } $$

For minimum dipole moment, $$n = 1$$, which gives, $$\mu =\dfrac { eh }{ 4\pi m } $$
Question 12
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The permanent magnetic moment of the atoms of a material is not zero. The material :

A
must be paramagnetic

B
must be diamagnetic

C
must be ferromagnetic

D
may be paramagnetic

Solution

Unlike paramagnetic materials, the atomic moments in ferromagnetic materials exhibit very strong interactions. These interactions are produced by electronic exchange forces and result in a parallel or antiparallel alignment of atomic moments.
This results in permanent non-zero magnetic moment of atoms in these materials.
Question 13
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Magnetic moment of bar magnet is $$M$$. The work done in turning the magnet by $$90^o$$ in direction of magnetic field $$B$$ will be

A
Zero

B
$$\displaystyle\frac{1}{2}$$$$MB$$

C
$$3$$$$MB$$

D
$$MB$$

Solution

Potential energy of a magnetic moment at an angle $$\theta$$ with the magnetic field = $$-MB\cos\theta$$
Thus work done in rotating from angle $$\theta_1$$ to $$\theta_2=MB(cos\theta_1-cos\theta_2)$$
$$=MB(cos0^{\circ}-cos90^{\circ})$$
$$=MB(1-0)$$
$$=MB$$
Question 14
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A magnet of magnetic moment $$20\ CGS$$ units is freely suspended in a uniform magnetic field of intensity $$0.3\ CGS$$ units. The moment of work done in deflecting it by an angle of $$30^{\circ}$$ in $$CGS$$ units is

A
$$6$$

B
$$3\ \sqrt {3}$$

C
$$3(2 - \sqrt {3})$$

D
$$3$$

Solution

Work done, $$W = MB (1 - \cos \theta)$$
$$= 20\times 0.3(1 - \cos 30^{\circ})$$
$$= 6\times \left (1 - \dfrac { {\sqrt{3}}}{2}\right ) = 3(2 - \sqrt {3})$$.
Question 15
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A bar magnet placed in non-uniform magnetic field experiences.

A
Only torque

B
Only force

C
Both torque and force

D
Neither force not torque

Solution

In a non-uniform magnetic field, bar magnet will experience both torque and force.

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Magnetism and Matter Test -14

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Question 1

Magnetic moment per unit volume

Magnetic induction force acting on a unit magnetic pole

Number of lines of force crossing per unit area

Number of lines of force crossing per unit volume

Solution

Question 2

A

B

C

D

Solution

Question 3

Constant

Zero

Infinity

Depends on magnetic field

Solution

Question 4

M

M/2

2M

0

Solution

Question 5

N

N/A−m

A − m

T

Solution

Question 6

$$14.76$$A

$$7.14$$A

$$11.32$$A

$$5.98$$A

Solution

Question 7

$$M\propto \omega$$

$$M\propto \omega^{2}$$

$$M\propto \sqrt {\omega}$$

None of these

Solution

Question 8

$${ \mu }_{ r }>1,{ \chi }_{ m }>1$$

$${ \mu }_{ r }>1,{ \chi }_{ m }<1$$

$${ \mu }_{ r }<1,{ \chi }_{ m }<0$$

$${ \mu }_{ r }<1,{ \chi }_{ m }>0$$

Solution

Question 9

Momentum

Collision

Voltage

Energy

Solution

Question 10

$$\mu \propto n$$

$$\mu \propto 1/n$$

$$\mu \propto n^2$$

$$\mu \propto 1/n^2$$

Solution

Question 11

$$\dfrac { eh }{ 2\pi m } $$

$$\dfrac { eh }{ 4\pi m } $$

$$\dfrac { eh }{ \pi m } $$

0

Solution

Question 12

must be paramagnetic

must be diamagnetic

must be ferromagnetic

may be paramagnetic

Solution