NEET Physics PYQ: Magnetism and Matter Topic-Wise Questions

Q 1 :
The magnetic potential energy, when a magnetic bar of magnetic moment $\vec{m}$ is placed perpendicular to the magnetic field $\vec{B}$ is [2024]

$- \frac{m B}{2}$
zero
$- m B$
$m B$

1

2

3

4

(2)

The magnetic potential energy is given by

$V = - \vec{m} \cdot \vec{B} = - m B \cos θ$

when, $θ = 90 °;$ $V = - m B \cos 90 ° = 0$

Q 2 :
The magnetic moment of an iron bar is $M$ . It is now bent in such a way that it forms an arc section of a circle subtending an angle of $60 °$ at the centre. The magnetic moment of this arc section is [2024]

$\frac{3 M}{π}$
$\frac{4 M}{π}$
$\frac{M}{π}$
$\frac{2 M}{π}$

1

2

3

4

(1)

Let the length of the iron bar be $L$ .
The magnetic moment of bar is given by

$M = m L$ ...(i)

Where, $m$ is pole strength.

When the bar is bent in the form of an arc,

$L = \frac{θ}{360} \times 2 π r = \frac{60 °}{360 °} \times 2 π r$

$L = \frac{π r}{3} \Rightarrow r = \frac{3 L}{π}$

From $∆ P Q S$ in the figure,

$\sin 30 ° = \frac{x}{r} \Rightarrow x = \frac{r}{2}$

Distance between $P R = 2 x = r$

New magnetic moment

$M' = m \times r$

$\Rightarrow m \times (\frac{3 L}{π}); M' = \frac{3 m L}{π}$

From equation (i), $M' = \frac{3 M}{π}$

Q 3 :
The magnetic moment and moment of inertia of a magnetic needle as shown are, respectively, $1.0 \times 10^{- 2}$ $A$ $m^{2}$ and $\frac{10^{- 6}}{π^{2}}$ $kg$ $m^{2} .$

If it completes 10 oscillations in 10 s, the magnitude of the magnetic field is [2024]

0.4 T
4 T
0.4 mT
4 mT

1

2

3

4

(3)

Magnetic moment, $M = 1.0 \times 10^{- 2} {Am}^{2}$

Moment of inertia, $I = \frac{10^{- 6}}{π^{2}}$ $kg$ $m^{2}$

Time period for one oscillation $\frac{10}{10} = 1$ $s$

We know that, $T = 2 π \sqrt{\frac{I}{M B}}$

$∴$ $T^{2} = \frac{4 π^{2} I}{M B}$

$B = \frac{4 π^{2} I}{M T^{2}} = \frac{4 \times {(3.14)}^{2}}{1 \times 10^{- 2}} \times \frac{10^{- 6}}{{(3.14)}^{2}} = 4 \times 10^{- 4} = 0.4$ $mT$

Q 4 :
In a uniform magnetic field of $0.049$ $T$ , a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is $9.8 \times 10^{- 6}$ $kg$ $m^{2}$ . If the magnitude of magnetic moment of the needle is $x \times 10^{- 5}$ ${Am}^{2}$ , then the value of $' x'$ is [2024]

$5 π^{2}$
$128 π^{2}$
$50 π^{2}$
$1280 π^{2}$

1

2

3

4

(4)

Time period of the needle, $T = \frac{5}{20} = \frac{1}{4}$ $s$

Given, $I = 9.8 \times 10^{- 6} kg$ $m^{2}, M = x \times 10^{- 5}$ ${Am}^{2}, B = 0.049$ $T$

Since, $T = 2 π \sqrt{\frac{I}{M B}}$

$\Rightarrow \frac{1}{4} = 2 π \sqrt{\frac{9.8 \times 10^{- 6}}{x \times 10^{- 5} \times 0.049}} \Rightarrow \frac{1}{8 π} = \sqrt{\frac{9.8 \times 10^{- 6}}{x \times 10^{- 5} \times 0.049}}$

$\Rightarrow \frac{1}{64 π^{2}} = \frac{9.8 \times 10^{- 6}}{x \times 10^{- 5} \times 0.049}$

$\Rightarrow x = 64 π^{2} \times \frac{9.8 \times 10^{- 1}}{0.049} = 1280 π^{2}$

Q 5 :
An iron bar of length $L$ has magnetic moment $M$ . It is bent at the middle of its length such that the two arms make an angle $60 °$ with each other. The magnetic moment of this new magnet is [2024]

$M$
$\frac{M}{2}$
$2$ $M$
$\frac{M}{\sqrt{3}}$

1

2

3

4

(2)

$M_{net} = \sqrt{{(\frac{M}{2})}^{2} + {(\frac{M}{2})}^{2} + 2 \frac{M}{2} \cdot \frac{M}{2} \cos 120 °}$

$M_{net} = \sqrt{\frac{M^{2}}{4} \times 2 - \frac{M^{2}}{4}} = \sqrt{\frac{M^{2}}{4}} = \frac{M}{2}$

Q 6 :
A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 $μ A$ and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by $180 °$ against the torque is [2017]

4.55 $μJ$
2.3 $μJ$
1.15 $μJ$
9.1 $μJ$

1

2

3

4

(4)

Work done in a coil

$W = m B (\cos θ_{1} - \cos θ_{2})$

When it is rotated by angle $180 °$ , then

$W = 2 m B = 2 (N I A) B$ ...(i)

Given, $N = 250, I = 85 μ A = 85 \times 10^{- 6} A$

$A = 1.25 \times 2.1 \times 10^{- 4} m^{2} \approx 2.6 \times 10^{- 4} m^{2}$

$B = 0.85$ $T$

Putting these values in eqn. (i), we get

$W = 2 \times 250 \times 85 \times 10^{- 6} \times 2.6 \times 10^{- 4} \times 0.85$

$\approx 9.1 \times 10^{- 6} J = 9.1$ $μ J$

Q 7 :
A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by 60° is W. Now the torque required to keep the magnet in this new position is [2016]

$\frac{W}{\sqrt{3}}$
$\sqrt{3} W$
$\frac{\sqrt{3} W}{2}$
$\frac{2 W}{\sqrt{3}}$

1

2

3

4

(2)

At equilibrium, potential energy of dipole

$U_{i} = - M B_{H}$

Final potential energy of dipole, $U_{f} = - M B_{H} \cos 60 ° = - \frac{M B_{H}}{2}$

$W = U_{f} - U_{i} = - \frac{M B_{H}}{2} - (- M B_{H}) = \frac{M B_{H}}{2}$ ...(i)

$τ = M B_{H} \sin 60 ° = 2 W \times \frac{\sqrt{3}}{2} [Using eqn. (i)]$

$= \sqrt{3} W$

Q 8 :
Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment $\vec{m}$ . Which configuration has highest net magnetic dipole moment? [2014]

(1)
(2)
(3)
(4)

1

2

3

4

(3)

The direction of magnetic dipole moment is from south to north pole of the magnet.

In configuration (1),

$m_{net} = \sqrt{m^{2} + m^{2} + 2 m m \cos 90 °} = \sqrt{m^{2} + m^{2}} = m \sqrt{2}$

In configuration (2),

In configuration (3),

$m_{net} = \sqrt{m^{2} + m^{2} + 2 m m \cos 30 °} = \sqrt{2 m^{2} + 2 m^{2} (\frac{\sqrt{3}}{2})} = m \sqrt{2 + \sqrt{3}}$

In configuration (4),

$m_{net} = \sqrt{m^{2} + m^{2} + 2 m m \cos 60 °} = \sqrt{2 m^{2} + 2 m^{2} (\frac{1}{2})} = m \sqrt{3}$

Topic Question Set

Q 1 :
The magnetic potential energy, when a magnetic bar of magnetic moment $\vec{m}$ is placed perpendicular to the magnetic field $\vec{B}$ is [2024]

Q 2 :
The magnetic moment of an iron bar is $M$ . It is now bent in such a way that it forms an arc section of a circle subtending an angle of $60 °$ at the centre. The magnetic moment of this arc section is [2024]

Q 3 :
The magnetic moment and moment of inertia of a magnetic needle as shown are, respectively, $1.0 \times 10^{- 2}$ $A$ $m^{2}$ and $\frac{10^{- 6}}{π^{2}}$ $kg$ $m^{2} .$

If it completes 10 oscillations in 10 s, the magnitude of the magnetic field is [2024]

Q 5 :
An iron bar of length $L$ has magnetic moment $M$ . It is bent at the middle of its length such that the two arms make an angle $60 °$ with each other. The magnetic moment of this new magnet is [2024]

Q 6 :
A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 $μ A$ and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by $180 °$ against the torque is [2017]

Q 7 :
A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by 60° is W. Now the torque required to keep the magnet in this new position is [2016]

Q 8 :
Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment $\vec{m}$ . Which configuration has highest net magnetic dipole moment? [2014]

Want Us to Email you About Special Offers & Updates?

Topic Question Set

Q 1 : The magnetic potential energy, when a magnetic bar of magnetic moment m→ is placed perpendicular to the magnetic field B→ is [2024]

Q 2 : The magnetic moment of an iron bar is M. It is now bent in such a way that it forms an arc section of a circle subtending an angle of 60° at the centre. The magnetic moment of this arc section is [2024]

Q 3 : The magnetic moment and moment of inertia of a magnetic needle as shown are, respectively, 1.0×10-2A m2 and 10-6π2 kg m2. If it completes 10 oscillations in 10 s, the magnitude of the magnetic field is [2024]

Q 4 : In a uniform magnetic field of 0.049 T, a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is 9.8×10-6kgm2. If the magnitude of magnetic moment of the needle is x×10-5Am2, then the value of 'x' is [2024]

Q 5 : An iron bar of length L has magnetic moment M. It is bent at the middle of its length such that the two arms make an angle 60° with each other. The magnetic moment of this new magnet is [2024]

Q 6 : A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 μA and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by 180° against the torque is [2017]

Q 7 : A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by 60° is W. Now the torque required to keep the magnet in this new position is [2016]

Q 8 : Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment m→. Which configuration has highest net magnetic dipole moment? [2014]

Want Us to Email you About Special Offers & Updates?

Q 1 :
The magnetic potential energy, when a magnetic bar of magnetic moment $\vec{m}$ is placed perpendicular to the magnetic field $\vec{B}$ is [2024]

Q 2 :
The magnetic moment of an iron bar is $M$ . It is now bent in such a way that it forms an arc section of a circle subtending an angle of $60 °$ at the centre. The magnetic moment of this arc section is [2024]

Q 3 :
The magnetic moment and moment of inertia of a magnetic needle as shown are, respectively, $1.0 \times 10^{- 2}$ $A$ $m^{2}$ and $\frac{10^{- 6}}{π^{2}}$ $kg$ $m^{2} .$

If it completes 10 oscillations in 10 s, the magnitude of the magnetic field is [2024]

Q 5 :
An iron bar of length $L$ has magnetic moment $M$ . It is bent at the middle of its length such that the two arms make an angle $60 °$ with each other. The magnetic moment of this new magnet is [2024]

Q 6 :
A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 $μ A$ and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by $180 °$ against the torque is [2017]

Q 7 :
A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by 60° is W. Now the torque required to keep the magnet in this new position is [2016]

Q 8 :
Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment $\vec{m}$ . Which configuration has highest net magnetic dipole moment? [2014]