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PHXII05:MAGNETISM and MATTER

360392 Two identical magnets with a length $10 c m$ and weight $50 g$ for each are arranged freely with their like poles facing in a vertical glass tube as shown in figure.
supporting img
The upper magnet in the air above the lower one so that the distance between the nearest poles of the magnets is $3 m m .$ Determine the pole strength of the poles of these magnets.

1

4.65 A m

2

8.64 A m

3

6.64 A m

4

3.54 A m

Explanation:

Since lengths of both the magnets are quite large as compared to separation between them, the interaction is effective only between their $N$ -poles.
Let $m$ be the strength of each pole of the two magnets. Then,
$\frac{μ_{0}}{4 π} \cdot \frac{m \times m}{r^{2}} =$ weight of the magnet
Here, weight of the magnet $= 50 g f = 50 \times 10^{- 3} k g f$
$= 50 \times 10^{- 3} \times 9.8 N$
and $r = 3 m m = 3 \times 10^{- 3} m$
$∵ \frac{10^{- 7} \times m^{2}}{{(3 \times 10^{- 3})}^{2}} = 50 \times 10^{- 3} \times 9.8$
or $m = 6.64 A m$

PHXII05:MAGNETISM and MATTER

360393 Force between two identical short bar magnets whose centres are $r$ metre apart is 8.1 $N$ , when their axes are along the same line. If separation is incresed to 3 $r$ and the axis are rearranged perpendicularly, the force between them would become

1 0.1

N

2 2.4

N

3 0.05

N

4 1.2

N

Explanation:

When axes are in the same line, the force between magnets
$F_{1} = \frac{μ_{0}}{4 π} \frac{6 M_{1} M_{2}}{r^{4}}$
when axes are $⊥$
$F_{2} = \frac{μ_{0}}{4 π} \frac{3 M_{1} M_{2}}{(3 r)^{4}}$
Therefore, $\frac{F_{1}}{F_{2}} = \frac{6 {(3)}^{4}}{3} \Rightarrow F_{2} = 0.05 N$

PHXII05:MAGNETISM and MATTER

360394 The figure shows various positions (labelled by subscripts) of small magnetised needles $P$ and $Q$ . The arrows show the direction of their magnetic moment. Which configuration corresponds to the lowest potential energy among all the configurations shown
supporting img

1

P Q_{3}

2

P Q_{5}

3

P Q_{4}

4

P Q_{6}

Explanation:

For $P Q_{6}$ combination angle between $\bar{M}$ and $\bar{B}$ is $0^{\circ}$ so that $U = (-)$ ve
$P Q_{6}$ corresponds to the lowest potential energy among all the configurations shown.

PHXII05:MAGNETISM and MATTER

360395 The magnetic energy density has the form

1

\frac{Δ B \cdot H}{2}

2

\frac{B . H}{2}

3

\frac{\bar{B} \cdot \bar{H}}{μ}

4

\frac{Δ B \times H}{2}

Explanation:

Magnetic energy density
$\frac{B^{2}}{2 μ_{0}} = \frac{B . (\frac{B}{μ_{0}})}{2} = \frac{B \cdot H}{2} .$

PHXII05:MAGNETISM and MATTER

360392 Two identical magnets with a length $10 c m$ and weight $50 g$ for each are arranged freely with their like poles facing in a vertical glass tube as shown in figure.
supporting img
The upper magnet in the air above the lower one so that the distance between the nearest poles of the magnets is $3 m m .$ Determine the pole strength of the poles of these magnets.

1

4.65 A m

2

8.64 A m

3

6.64 A m

4

3.54 A m

Explanation:

Since lengths of both the magnets are quite large as compared to separation between them, the interaction is effective only between their $N$ -poles.
Let $m$ be the strength of each pole of the two magnets. Then,
$\frac{μ_{0}}{4 π} \cdot \frac{m \times m}{r^{2}} =$ weight of the magnet
Here, weight of the magnet $= 50 g f = 50 \times 10^{- 3} k g f$
$= 50 \times 10^{- 3} \times 9.8 N$
and $r = 3 m m = 3 \times 10^{- 3} m$
$∵ \frac{10^{- 7} \times m^{2}}{{(3 \times 10^{- 3})}^{2}} = 50 \times 10^{- 3} \times 9.8$
or $m = 6.64 A m$

PHXII05:MAGNETISM and MATTER

360393 Force between two identical short bar magnets whose centres are $r$ metre apart is 8.1 $N$ , when their axes are along the same line. If separation is incresed to 3 $r$ and the axis are rearranged perpendicularly, the force between them would become

1 0.1

N

2 2.4

N

3 0.05

N

4 1.2

N

Explanation:

When axes are in the same line, the force between magnets
$F_{1} = \frac{μ_{0}}{4 π} \frac{6 M_{1} M_{2}}{r^{4}}$
when axes are $⊥$
$F_{2} = \frac{μ_{0}}{4 π} \frac{3 M_{1} M_{2}}{(3 r)^{4}}$
Therefore, $\frac{F_{1}}{F_{2}} = \frac{6 {(3)}^{4}}{3} \Rightarrow F_{2} = 0.05 N$

PHXII05:MAGNETISM and MATTER

360394 The figure shows various positions (labelled by subscripts) of small magnetised needles $P$ and $Q$ . The arrows show the direction of their magnetic moment. Which configuration corresponds to the lowest potential energy among all the configurations shown
supporting img

1

P Q_{3}

2

P Q_{5}

3

P Q_{4}

4

P Q_{6}

Explanation:

For $P Q_{6}$ combination angle between $\bar{M}$ and $\bar{B}$ is $0^{\circ}$ so that $U = (-)$ ve
$P Q_{6}$ corresponds to the lowest potential energy among all the configurations shown.

PHXII05:MAGNETISM and MATTER

360395 The magnetic energy density has the form

1

\frac{Δ B \cdot H}{2}

2

\frac{B . H}{2}

3

\frac{\bar{B} \cdot \bar{H}}{μ}

4

\frac{Δ B \times H}{2}

Explanation:

Magnetic energy density
$\frac{B^{2}}{2 μ_{0}} = \frac{B . (\frac{B}{μ_{0}})}{2} = \frac{B \cdot H}{2} .$

PHXII05:MAGNETISM and MATTER

360392 Two identical magnets with a length $10 c m$ and weight $50 g$ for each are arranged freely with their like poles facing in a vertical glass tube as shown in figure.
supporting img
The upper magnet in the air above the lower one so that the distance between the nearest poles of the magnets is $3 m m .$ Determine the pole strength of the poles of these magnets.

1

4.65 A m

2

8.64 A m

3

6.64 A m

4

3.54 A m

Explanation:

Since lengths of both the magnets are quite large as compared to separation between them, the interaction is effective only between their $N$ -poles.
Let $m$ be the strength of each pole of the two magnets. Then,
$\frac{μ_{0}}{4 π} \cdot \frac{m \times m}{r^{2}} =$ weight of the magnet
Here, weight of the magnet $= 50 g f = 50 \times 10^{- 3} k g f$
$= 50 \times 10^{- 3} \times 9.8 N$
and $r = 3 m m = 3 \times 10^{- 3} m$
$∵ \frac{10^{- 7} \times m^{2}}{{(3 \times 10^{- 3})}^{2}} = 50 \times 10^{- 3} \times 9.8$
or $m = 6.64 A m$

PHXII05:MAGNETISM and MATTER

360393 Force between two identical short bar magnets whose centres are $r$ metre apart is 8.1 $N$ , when their axes are along the same line. If separation is incresed to 3 $r$ and the axis are rearranged perpendicularly, the force between them would become

1 0.1

N

2 2.4

N

3 0.05

N

4 1.2

N

Explanation:

When axes are in the same line, the force between magnets
$F_{1} = \frac{μ_{0}}{4 π} \frac{6 M_{1} M_{2}}{r^{4}}$
when axes are $⊥$
$F_{2} = \frac{μ_{0}}{4 π} \frac{3 M_{1} M_{2}}{(3 r)^{4}}$
Therefore, $\frac{F_{1}}{F_{2}} = \frac{6 {(3)}^{4}}{3} \Rightarrow F_{2} = 0.05 N$

PHXII05:MAGNETISM and MATTER

360394 The figure shows various positions (labelled by subscripts) of small magnetised needles $P$ and $Q$ . The arrows show the direction of their magnetic moment. Which configuration corresponds to the lowest potential energy among all the configurations shown
supporting img

1

P Q_{3}

2

P Q_{5}

3

P Q_{4}

4

P Q_{6}

Explanation:

For $P Q_{6}$ combination angle between $\bar{M}$ and $\bar{B}$ is $0^{\circ}$ so that $U = (-)$ ve
$P Q_{6}$ corresponds to the lowest potential energy among all the configurations shown.

PHXII05:MAGNETISM and MATTER

360395 The magnetic energy density has the form

1

\frac{Δ B \cdot H}{2}

2

\frac{B . H}{2}

3

\frac{\bar{B} \cdot \bar{H}}{μ}

4

\frac{Δ B \times H}{2}

Explanation:

Magnetic energy density
$\frac{B^{2}}{2 μ_{0}} = \frac{B . (\frac{B}{μ_{0}})}{2} = \frac{B \cdot H}{2} .$

PHXII05:MAGNETISM and MATTER

360392 Two identical magnets with a length $10 c m$ and weight $50 g$ for each are arranged freely with their like poles facing in a vertical glass tube as shown in figure.
supporting img
The upper magnet in the air above the lower one so that the distance between the nearest poles of the magnets is $3 m m .$ Determine the pole strength of the poles of these magnets.

1

4.65 A m

2

8.64 A m

3

6.64 A m

4

3.54 A m

Explanation:

Since lengths of both the magnets are quite large as compared to separation between them, the interaction is effective only between their $N$ -poles.
Let $m$ be the strength of each pole of the two magnets. Then,
$\frac{μ_{0}}{4 π} \cdot \frac{m \times m}{r^{2}} =$ weight of the magnet
Here, weight of the magnet $= 50 g f = 50 \times 10^{- 3} k g f$
$= 50 \times 10^{- 3} \times 9.8 N$
and $r = 3 m m = 3 \times 10^{- 3} m$
$∵ \frac{10^{- 7} \times m^{2}}{{(3 \times 10^{- 3})}^{2}} = 50 \times 10^{- 3} \times 9.8$
or $m = 6.64 A m$

PHXII05:MAGNETISM and MATTER

360393 Force between two identical short bar magnets whose centres are $r$ metre apart is 8.1 $N$ , when their axes are along the same line. If separation is incresed to 3 $r$ and the axis are rearranged perpendicularly, the force between them would become

1 0.1

N

2 2.4

N

3 0.05

N

4 1.2

N

Explanation:

When axes are in the same line, the force between magnets
$F_{1} = \frac{μ_{0}}{4 π} \frac{6 M_{1} M_{2}}{r^{4}}$
when axes are $⊥$
$F_{2} = \frac{μ_{0}}{4 π} \frac{3 M_{1} M_{2}}{(3 r)^{4}}$
Therefore, $\frac{F_{1}}{F_{2}} = \frac{6 {(3)}^{4}}{3} \Rightarrow F_{2} = 0.05 N$

PHXII05:MAGNETISM and MATTER

360394 The figure shows various positions (labelled by subscripts) of small magnetised needles $P$ and $Q$ . The arrows show the direction of their magnetic moment. Which configuration corresponds to the lowest potential energy among all the configurations shown
supporting img

1

P Q_{3}

2

P Q_{5}

3

P Q_{4}

4

P Q_{6}

Explanation:

For $P Q_{6}$ combination angle between $\bar{M}$ and $\bar{B}$ is $0^{\circ}$ so that $U = (-)$ ve
$P Q_{6}$ corresponds to the lowest potential energy among all the configurations shown.

PHXII05:MAGNETISM and MATTER

360395 The magnetic energy density has the form

1

\frac{Δ B \cdot H}{2}

2

\frac{B . H}{2}

3

\frac{\bar{B} \cdot \bar{H}}{μ}

4

\frac{Δ B \times H}{2}

Explanation:

Magnetic energy density
$\frac{B^{2}}{2 μ_{0}} = \frac{B . (\frac{B}{μ_{0}})}{2} = \frac{B \cdot H}{2} .$

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