Tag: physics

Questions Related to physics

Among the following statements: 

A) In $\tan A$ position of deflection magnetometer $B$ and $B _{H}$ are perpendicular 

B) In $\tan B$ position of deflection magnetometer $B$ and $B _{H}$ parallel

uniform magnetic field lines of earth magnetism physics

  1. A true & B false

  2. A false & B true

  3. A and B are true

  4. A and B are false

Show answer
Correct Option: A
Explanation:

In $\tan A$ position , the arms are in east-west direction and the compass needle is in north-south direction and the bar magnet is kept parallel to the arms, perpendicular to the compass needle.

In $\tan B$ position , the arms are in north-south direction and the compass needle is in same direction , the magnet is kept in east - west direction , perpendicular to the compass needle.

The restoring couple for a magnet oscillating in the vibration magnetometer is provided by

uniform magnetic field lines of earth magnetism physics

  1. horizontal component of earths magnetic field

  2. gravity

  3. torsion in the suspended thread

  4. magnetic field of magnet

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Correct Option: A
Explanation:

When the bar magnet in vibration magnetometer is displaced from the earth's magnetic field , the torque acts on it to allign it with the earth's magnetic field . So the earth's magnetic field is  the restoring force.

Assertion (A) : In deflection magnetometer a short magnetic needle is arranged in the compass box
Reason (R) : The magnetic needle is found in the uniform magnetic field produced by earth and bar magnet
uniform magnetic field lines of earth magnetism physics

  1. Both A and R are true and R is the correct explanation of A

  2. Both A and R are true and R is not correct explanation of A

  3. A is true, But R is false

  4. A is false, But R is true

Show answer
Correct Option: A
Explanation:

In Deflection magnetometer ,the bar magnet is kept at a distance from the magnetic needle and the deflection thus observed is due to the earth's and bar magnet's magnetic field..

Deflection magnetometer is held in $\tan B$ position. A magnet placed on one of its arms produces no deflection. This implies that the axis of the magnet is

uniform magnetic field lines of earth magnetism physics

  1. in the east - west direction

  2. in the north-south direction

  3. perpendicular to the wooden bench

  4. North - East

Show answer
Correct Option: B
Explanation:

In $\tan B$ position , the arms are in the north south direction and the aluminium pointer are in east- west direction. So the compass needle is in north- south direction. For the magnetic field lines of the magnet to be ineffective then they must be in the north south direction so that they will not create a torque.

If the magnet is in east- west direction , a couple acts on the magnet and thus causes deflection.

The magnets of same magnetic moment $M$ and different lengths are placed in $tan\; A$ position. The fields at equal distances from them are :

uniform magnetic field lines of earth magnetism physics

  1. greater for long magnet

  2. greater for small magnet

  3. equal for both

  4. zero

Show answer
Correct Option: A
Explanation:

In tan A position , the magnetic field due to the bar magnet is given by
$\dfrac{\mu _o}{4 \pi} \dfrac{2Md}{(d^2 - l^2)^{3/2}} = B$ for a bar magnet
where $ l $ is the length of the magnet and $ d $ is the distance of the point from the centre of the magnet.
For the same distance $ d $ and the same magnetic moment, strength of the magnetic field
$ B \propto \dfrac{1}{(d^2-l^2)^\dfrac{3}{2}} $
So larger the length of the magnet, greater is the value of $ \dfrac{1}{(d^2-l^2)^\dfrac{3}{2}} $ and consequentially, the strength of the magnetic field.
So , magnetic field at a point is larger for long bar magnet

A D.M.M is in tan A position in a region where $B _H$  is 50$\mu $T. When a magnet is placed at a suitable distance the deflection obtained is 45$^{0}$. The resultant magnetic field at the centre of the compass is

uniform magnetic field lines of earth magnetism physics

  1. 50$\mu $T

  2. $50\sqrt{2}\mu \top $

  3. 25 $\mu $ T

  4. 100$\mu $ T

Show answer
Correct Option: B
Explanation:

The magnetic field due to the magnet is B $ = B _H  tan \theta $
$ B = B _H tan 45 = B _H$
Total magnetis field at the centre is 
$ B _T= \sqrt{B^2 + B _H ^2}= \sqrt{2}{B _H} $
$B _T = 50 \sqrt{2}\mu $T

To measure the magnetic moment of a bar magnet, one may use.

uniform magnetic field lines of earth magnetism physics

  1. a tangent galvanometer.

  2. a deflection galvanometer if the earth's horizontal field is known.

  3. an oscillation magnetometer if the earth's horizontal field is known.

  4. both deflection and oscillation magnetometer if the earth's horizontal field is not known.

Show answer
Correct Option: B,C,D
Explanation:

To measure the magnetic moment of a bar magnet,
a deflection galvanometer is used  if the earth's horizontal field is known.
An oscillation magnetometer  can be used if the earth's horizontal field is known.
Both deflection and oscillation magnetometer can be used  if the earth's horizontal field is not known since there are two variables.

When two magnets are placed $20\ \text{cms}$ and $15\ \text{cms}$ away on the two arms of a deflection magnetometer, it shows no deflection. The ration of magnetic moments is :

uniform magnetic field lines of earth magnetism physics

  1. $\displaystyle\dfrac{M _1}{M _2}=\dfrac{64}{27}$

  2. $\displaystyle\dfrac{M _1}{M _2}=\dfrac{4}{3}$

  3. $\displaystyle\dfrac{M _1}{M _2}=\dfrac{16}{9}$

  4. $\text{none of these}$

Show answer
Correct Option: A
Explanation:

Magnetic moment ratio,
$\dfrac{M _1}{M _2}=\dfrac{d _1^3}{d _2^3}$

$\Rightarrow \dfrac{M _1}{M _2}=\left(\dfrac{20}{15}\right)^3$
$\Rightarrow \dfrac{M _1}{M _2}=\left(\dfrac{4}{3}\right)^3$
$\Rightarrow \dfrac{M _1}{M _2}=\dfrac{64}{27}$

The factor on which the period of oscillation of a bar magnet in uniform magnetic field depends is

uniform magnetic field lines of earth magnetism physics

  1. nature of suspension fibre

  2. length of the suspension fibre

  3. vertical component of earths magnetic induction

  4. moment of inertia of the magnet

Show answer
Correct Option: D
Explanation:

The time period of oscillation is given by
$T =2 \pi \sqrt{ \dfrac{I}{mB _H} }$
Therefore $T $ is proportional to $ \sqrt{I}$

When a D.M. is set in $\tan A$ position, the deflection is $30^{o}$ for a magnet A placed at a distance of $40\ cm$ from the midpoint of the D.M. When the D.M. is kept in $\tan B$ position another magnet B produces a deflection of $60^{o}$, when placed at the same distance. The ratio of the magnetic moments of A and B is :

uniform magnetic field lines of earth magnetism physics

  1. $1 : 2$

  2. $1 : 3$

  3. $2 : 3$

  4. $1 : 6$

Show answer
Correct Option: D
Explanation:

The deflection off the magnetic needle in tan A position by a short magnet is given by 

$\dfrac{\mu _o}{4 \pi} \dfrac{2M _A}{d^3} = B _H \tan \theta _A  $

The deflection off the magnetic needle in tan B position by a short magnet is given by 

$\dfrac{\mu _o}{4 \pi} \dfrac{M _B}{d^3} = B _H \tan \theta _B  $

$\dfrac{ \tan \theta _A}{\tan \theta _B} = \dfrac{2 M _A}{M _B} $

$ \dfrac{M _A}{M _B} =\dfrac{1}{2} \times   \dfrac{\tan 30}{\tan 60}  = \dfrac{1}{6} $