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PHXII05:MAGNETISM and MATTER

360631 At a certain place, the angle of dip is $30^{\circ}$ and the horizontal component of earth's magnetic field 0.50 oerested. The earth's total magnetic field (in oerested) is

1

\sqrt{3}

2 1

3

\frac{1}{\sqrt{3}}

4

\frac{1}{2}

Explanation:

$B = \frac{H}{\cos θ} = \frac{0.50}{\cos 30^{\circ}} = \frac{0.50 \times 2}{\sqrt{3}} = 1 / \sqrt{3}$
So, correct option is (3).

MHTCET - 2021

PHXII05:MAGNETISM and MATTER

360632 Statement A :
Magnetic field strength at a point on axial line of a bar magnet is along south to north pole of magnet.
Statement B :
The magnetic filed strength can never be along north to south pole of a magnet.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both statements are correct.

4 Both Statements are incorrect.

PHXII05:MAGNETISM and MATTER

360633 The force experienced by a pole of strength 100 $A m$ at a distance of 0.2 $m$ from a short magnet of length 5 $c m$ and pole strength of 200 $A m$ on its axial line will be

1

2.5 \times 10^{- 3} N

2

2.5 \times 10^{- 2} N

3

5.0 \times 10^{- 3} N

4

5.0 \times 10^{- 2} N

Explanation:

$F = m B = \frac{μ_{0}}{4 π} \frac{2 m^{'} ℓ}{x^{3}} m$
$= \frac{10^{- 7} \times 2 \times 200 \times 0.05 \times 100}{8 \times 10^{- 3}}$
$= 2.5 \times 10^{- 2} N$

PHXII05:MAGNETISM and MATTER

360634 The ratio of magnetic fields due to a bar magnet at the two axial points $P_{1}$ and $P_{2}$ which are separated from each other by 10 $c m$ is $25 : 2$ . Point $P_{1}$ is situated at 10 $c m$ from the centre of the magnet. Magnetic length of the bar magnet is (points $P_{1}$ and $P_{2}$ are on the same side of magnet and distance of $P_{2}$ from the centre is greater than distance of $P_{1}$ from the centre of magnet)

1 5

c m

2 10

c m

3 15

c m

4 20

c m

Explanation:

Let magentic field at $P_{1}$ is $B_{1}$ and at $P_{2}$ is $B_{2}$
supporting img
$∴ \frac{B_{1}}{B_{2}} = \frac{\frac{x_{1}}{{(x_{1}^{2} - l^{2})}^{2}}}{\frac{x_{2}}{{(x_{2}^{2} - l^{2})}^{2}}} = \frac{{(x_{2}^{2} - l^{2})}^{2}}{{(x_{1}^{2} - l^{2})}^{2}} \times \frac{x_{1}}{x_{2}}$
$\Rightarrow \frac{25}{2} = \frac{10}{20} {[\frac{x_{2}^{2} - l^{2}}{x_{1}^{2} - l^{2}}]}^{2}$
or ${[\frac{x_{2}^{2} - l^{2}}{x_{1}^{2} - l^{2}}]}^{2} = 5$
or $x_{2}^{2} - l^{2} = 5 x_{1}^{2} - 5 l^{2}$
or $4 l^{2} = 5 x_{1}^{2} - x_{2}^{2}$
$= 5 \times (10)^{2} - (20)^{2}$
$= 500 - 400 = 100$
$\Rightarrow l^{2} = 25$
$\Rightarrow l = 5 c m$
Therefore, $2 l = 10 c m$

PHXII05:MAGNETISM and MATTER

360631 At a certain place, the angle of dip is $30^{\circ}$ and the horizontal component of earth's magnetic field 0.50 oerested. The earth's total magnetic field (in oerested) is

1

\sqrt{3}

2 1

3

\frac{1}{\sqrt{3}}

4

\frac{1}{2}

Explanation:

$B = \frac{H}{\cos θ} = \frac{0.50}{\cos 30^{\circ}} = \frac{0.50 \times 2}{\sqrt{3}} = 1 / \sqrt{3}$
So, correct option is (3).

MHTCET - 2021

PHXII05:MAGNETISM and MATTER

360632 Statement A :
Magnetic field strength at a point on axial line of a bar magnet is along south to north pole of magnet.
Statement B :
The magnetic filed strength can never be along north to south pole of a magnet.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both statements are correct.

4 Both Statements are incorrect.

PHXII05:MAGNETISM and MATTER

360633 The force experienced by a pole of strength 100 $A m$ at a distance of 0.2 $m$ from a short magnet of length 5 $c m$ and pole strength of 200 $A m$ on its axial line will be

1

2.5 \times 10^{- 3} N

2

2.5 \times 10^{- 2} N

3

5.0 \times 10^{- 3} N

4

5.0 \times 10^{- 2} N

Explanation:

$F = m B = \frac{μ_{0}}{4 π} \frac{2 m^{'} ℓ}{x^{3}} m$
$= \frac{10^{- 7} \times 2 \times 200 \times 0.05 \times 100}{8 \times 10^{- 3}}$
$= 2.5 \times 10^{- 2} N$

PHXII05:MAGNETISM and MATTER

360634 The ratio of magnetic fields due to a bar magnet at the two axial points $P_{1}$ and $P_{2}$ which are separated from each other by 10 $c m$ is $25 : 2$ . Point $P_{1}$ is situated at 10 $c m$ from the centre of the magnet. Magnetic length of the bar magnet is (points $P_{1}$ and $P_{2}$ are on the same side of magnet and distance of $P_{2}$ from the centre is greater than distance of $P_{1}$ from the centre of magnet)

1 5

c m

2 10

c m

3 15

c m

4 20

c m

Explanation:

Let magentic field at $P_{1}$ is $B_{1}$ and at $P_{2}$ is $B_{2}$
supporting img
$∴ \frac{B_{1}}{B_{2}} = \frac{\frac{x_{1}}{{(x_{1}^{2} - l^{2})}^{2}}}{\frac{x_{2}}{{(x_{2}^{2} - l^{2})}^{2}}} = \frac{{(x_{2}^{2} - l^{2})}^{2}}{{(x_{1}^{2} - l^{2})}^{2}} \times \frac{x_{1}}{x_{2}}$
$\Rightarrow \frac{25}{2} = \frac{10}{20} {[\frac{x_{2}^{2} - l^{2}}{x_{1}^{2} - l^{2}}]}^{2}$
or ${[\frac{x_{2}^{2} - l^{2}}{x_{1}^{2} - l^{2}}]}^{2} = 5$
or $x_{2}^{2} - l^{2} = 5 x_{1}^{2} - 5 l^{2}$
or $4 l^{2} = 5 x_{1}^{2} - x_{2}^{2}$
$= 5 \times (10)^{2} - (20)^{2}$
$= 500 - 400 = 100$
$\Rightarrow l^{2} = 25$
$\Rightarrow l = 5 c m$
Therefore, $2 l = 10 c m$

PHXII05:MAGNETISM and MATTER

360631 At a certain place, the angle of dip is $30^{\circ}$ and the horizontal component of earth's magnetic field 0.50 oerested. The earth's total magnetic field (in oerested) is

1

\sqrt{3}

2 1

3

\frac{1}{\sqrt{3}}

4

\frac{1}{2}

Explanation:

$B = \frac{H}{\cos θ} = \frac{0.50}{\cos 30^{\circ}} = \frac{0.50 \times 2}{\sqrt{3}} = 1 / \sqrt{3}$
So, correct option is (3).

MHTCET - 2021

PHXII05:MAGNETISM and MATTER

360632 Statement A :
Magnetic field strength at a point on axial line of a bar magnet is along south to north pole of magnet.
Statement B :
The magnetic filed strength can never be along north to south pole of a magnet.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both statements are correct.

4 Both Statements are incorrect.

PHXII05:MAGNETISM and MATTER

360633 The force experienced by a pole of strength 100 $A m$ at a distance of 0.2 $m$ from a short magnet of length 5 $c m$ and pole strength of 200 $A m$ on its axial line will be

1

2.5 \times 10^{- 3} N

2

2.5 \times 10^{- 2} N

3

5.0 \times 10^{- 3} N

4

5.0 \times 10^{- 2} N

Explanation:

$F = m B = \frac{μ_{0}}{4 π} \frac{2 m^{'} ℓ}{x^{3}} m$
$= \frac{10^{- 7} \times 2 \times 200 \times 0.05 \times 100}{8 \times 10^{- 3}}$
$= 2.5 \times 10^{- 2} N$

PHXII05:MAGNETISM and MATTER

360634 The ratio of magnetic fields due to a bar magnet at the two axial points $P_{1}$ and $P_{2}$ which are separated from each other by 10 $c m$ is $25 : 2$ . Point $P_{1}$ is situated at 10 $c m$ from the centre of the magnet. Magnetic length of the bar magnet is (points $P_{1}$ and $P_{2}$ are on the same side of magnet and distance of $P_{2}$ from the centre is greater than distance of $P_{1}$ from the centre of magnet)

1 5

c m

2 10

c m

3 15

c m

4 20

c m

Explanation:

Let magentic field at $P_{1}$ is $B_{1}$ and at $P_{2}$ is $B_{2}$
supporting img
$∴ \frac{B_{1}}{B_{2}} = \frac{\frac{x_{1}}{{(x_{1}^{2} - l^{2})}^{2}}}{\frac{x_{2}}{{(x_{2}^{2} - l^{2})}^{2}}} = \frac{{(x_{2}^{2} - l^{2})}^{2}}{{(x_{1}^{2} - l^{2})}^{2}} \times \frac{x_{1}}{x_{2}}$
$\Rightarrow \frac{25}{2} = \frac{10}{20} {[\frac{x_{2}^{2} - l^{2}}{x_{1}^{2} - l^{2}}]}^{2}$
or ${[\frac{x_{2}^{2} - l^{2}}{x_{1}^{2} - l^{2}}]}^{2} = 5$
or $x_{2}^{2} - l^{2} = 5 x_{1}^{2} - 5 l^{2}$
or $4 l^{2} = 5 x_{1}^{2} - x_{2}^{2}$
$= 5 \times (10)^{2} - (20)^{2}$
$= 500 - 400 = 100$
$\Rightarrow l^{2} = 25$
$\Rightarrow l = 5 c m$
Therefore, $2 l = 10 c m$

PHXII05:MAGNETISM and MATTER

360631 At a certain place, the angle of dip is $30^{\circ}$ and the horizontal component of earth's magnetic field 0.50 oerested. The earth's total magnetic field (in oerested) is

1

\sqrt{3}

2 1

3

\frac{1}{\sqrt{3}}

4

\frac{1}{2}

Explanation:

$B = \frac{H}{\cos θ} = \frac{0.50}{\cos 30^{\circ}} = \frac{0.50 \times 2}{\sqrt{3}} = 1 / \sqrt{3}$
So, correct option is (3).

MHTCET - 2021

PHXII05:MAGNETISM and MATTER

360632 Statement A :
Magnetic field strength at a point on axial line of a bar magnet is along south to north pole of magnet.
Statement B :
The magnetic filed strength can never be along north to south pole of a magnet.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both statements are correct.

4 Both Statements are incorrect.

PHXII05:MAGNETISM and MATTER

360633 The force experienced by a pole of strength 100 $A m$ at a distance of 0.2 $m$ from a short magnet of length 5 $c m$ and pole strength of 200 $A m$ on its axial line will be

1

2.5 \times 10^{- 3} N

2

2.5 \times 10^{- 2} N

3

5.0 \times 10^{- 3} N

4

5.0 \times 10^{- 2} N

Explanation:

$F = m B = \frac{μ_{0}}{4 π} \frac{2 m^{'} ℓ}{x^{3}} m$
$= \frac{10^{- 7} \times 2 \times 200 \times 0.05 \times 100}{8 \times 10^{- 3}}$
$= 2.5 \times 10^{- 2} N$

PHXII05:MAGNETISM and MATTER

360634 The ratio of magnetic fields due to a bar magnet at the two axial points $P_{1}$ and $P_{2}$ which are separated from each other by 10 $c m$ is $25 : 2$ . Point $P_{1}$ is situated at 10 $c m$ from the centre of the magnet. Magnetic length of the bar magnet is (points $P_{1}$ and $P_{2}$ are on the same side of magnet and distance of $P_{2}$ from the centre is greater than distance of $P_{1}$ from the centre of magnet)

1 5

c m

2 10

c m

3 15

c m

4 20

c m

Explanation:

Let magentic field at $P_{1}$ is $B_{1}$ and at $P_{2}$ is $B_{2}$
supporting img
$∴ \frac{B_{1}}{B_{2}} = \frac{\frac{x_{1}}{{(x_{1}^{2} - l^{2})}^{2}}}{\frac{x_{2}}{{(x_{2}^{2} - l^{2})}^{2}}} = \frac{{(x_{2}^{2} - l^{2})}^{2}}{{(x_{1}^{2} - l^{2})}^{2}} \times \frac{x_{1}}{x_{2}}$
$\Rightarrow \frac{25}{2} = \frac{10}{20} {[\frac{x_{2}^{2} - l^{2}}{x_{1}^{2} - l^{2}}]}^{2}$
or ${[\frac{x_{2}^{2} - l^{2}}{x_{1}^{2} - l^{2}}]}^{2} = 5$
or $x_{2}^{2} - l^{2} = 5 x_{1}^{2} - 5 l^{2}$
or $4 l^{2} = 5 x_{1}^{2} - x_{2}^{2}$
$= 5 \times (10)^{2} - (20)^{2}$
$= 500 - 400 = 100$
$\Rightarrow l^{2} = 25$
$\Rightarrow l = 5 c m$
Therefore, $2 l = 10 c m$

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