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Multiple choice uniform magnetic field lines of earth magnetism physics

Two magnets when placed in $\tan A$ position at the same distance cause deflections of $30^{o}$ and $60^{o}$. The ratio of their magnetic moments is :

  1. $3 : 1$
  2. $1 : 3$
  3. $1 : 2$
  4. $2 : 1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In $\tan A$ position , the deflection of the needle is given by

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

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

$\dfrac{M _A}{M _B} = \dfrac{1}{3} $

Multiple choice uniform magnetic field lines of earth magnetism physics

Vibration magnetometer works on the principle of

  1. torque acting on the bar magnet and rotational inertia

  2. force acting on the bar magnet and rotational inertia

  3. both the force and torque acting on the bar magnet

  4. neither force nor torque
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When the bar magnet in the deflection magnetometer is displaced , a torque acts on it due to the horizontal earth's magnetic filed. So the magnet vibrates and alligns parallel to the earth's magnetic field.

Multiple choice uniform magnetic field lines of earth magnetism physics

A short magnet when placed at a distance of $15 cm$ in $\tan A$ position produces a deflection of $60^{o}$. If the magnet is cut into $3$ equal parts and one of them is kept at the same distance in $\tan A$ position, the deflection is :

  1. $20^{o}$
  2. $30^{o}$
  3. $45^{o}$
  4. $60^{o}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The deflection of the magnetic needle in $\tan A$ position by a short magnet is given by 
$\dfrac{\mu _o}{4 \pi} \dfrac{2M}{d^3} = B _H \tan \theta _A  $

$ M _B = \dfrac{M}{3}$

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

$ \tan \theta _B = \dfrac{M _B}{M _A} \times \sqrt{3}$

$\theta _B = 30 ^o $

Multiple choice uniform magnetic field lines of earth magnetism physics

Two bar magnets of same size with magnetic moments M$ _{1}$ and M$ _{2}$ (M$ _{1}$ > M$ _{2}$ ) are simultaneously used at the tan A position in a DMM. When the magnets are placed with unlike poles in contact the deflection is 30$^{0}$ and when like poles are in contact the deflection is 60$^{0}$ . Then $\dfrac{M _{1}}{M _{2}} :$

  1. $\dfrac{3}{1}$
  2. $\dfrac{3}{4}$
  3. $\dfrac{6}{1}$
  4. $\dfrac{2}{1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
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}{d^3} = B _H tan \theta  $

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

$\dfrac{ tan \theta _A}{tan \theta _B} = \dfrac{M _1 - M _2}{M _1 + M _2} $

$  \dfrac{M _1 - M _2}{M _1 + M _2} = \dfrac{1}{3}$

$\dfrac{M _1}{M _2} = \dfrac{2}{1} $
Multiple choice uniform magnetic field lines of earth magnetism physics

Two bar magnets A and B are placed on the two arms of a deflection magnetometer. When their distances from the centre of the needle are 20 cm and 40 cm respectively, the needle lies in the magnetic meridian. If the moment of the magnet A is 100 Am$^{2}$, then the moment of the magnet B is:

  1. 400 Am$^{2}$
  2. 800 Am$^{2}$
  3. 1200 Am$^{2}$
  4. 1600 Am$^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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  $

Since the deflection is zero , 
$ \dfrac{M _A}{M _B} = \dfrac{d _A ^3}{d _B ^3}$

$\dfrac{M _A}{M _B}  = \dfrac{1}{8} $

$M _B = 800 A m^2 $
Multiple choice uniform magnetic field lines of earth magnetism physics

When a short bar magnet is kept at a distance of 20 cm from the centre of D.M., in Tan A position, the deflection is 45$^{0}$ . If $H=30$ A/m, the moment of the magnet is :

  1. 1.5 $\times $ 10$^{-2}$ Am$^{2}$
  2. 1.51Am$^{2}$
  3. 3.01Am$^{2}$
  4. 1.31Am$^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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  $

$\theta = 45 ^o $
$B = \mu _o \times H  $
$4 \pi \times 10^{-7} \times 30 = 10 ^{-7} \times \dfrac{2M}{d^3} $

$M = 1.51 Am^2 $

Multiple choice uniform magnetic field lines of earth magnetism physics

A short bar magnet is kept at a distance of 30 cm from the centre of the compass box on D.M, which is in Tan A position. The deflection is 45$^{0}$. If the horizontal component of earth's field strength is 30 A/m, the magnetic moment of the magnet is

  1. $0.128\pi Am^{2}$
  2. $1.28\pi Am^{2}$
  3. $128\pi Am^{2}$
  4. $12.8\pi Am^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In Tan A position, the magnetic field B = (mu_0 / 4pi) * (2M / d^3). Given B = B_H * tan(theta) and theta = 45 degrees, tan(45) = 1. Thus B = B_H = 30 A/m. Solving 30 = (10^-7) * (2M / (0.3)^3) yields M = 12.8 * pi Am^2.

Multiple choice uniform magnetic field lines of earth magnetism physics

The tangent of deflection of angle of the needle of a DMM, taken along the y-axis is plotted against the distance d between the needle and a short magnet. The slope of the curve varies as

  1. d
  2. d$^{-1}$
  3. d$^{2}$
  4. d$^{-3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The deflection of 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  $

$ \theta  = \dfrac{K}{d^3} $

Multiple choice uniform magnetic field lines of earth magnetism physics

The ratio of magnetic moments of two bar magnets is $5 : 2$. If the deflection produced by the first magnet in the D.M. in $\tan A$ position is $60^{o}$ , the deflection due to the second magnet kept at the same distance in tan A position is :

  1. greater than $45^{o}$
  2. less than $45^{o}$
  3. less than $30^{o}$
  4. greater than $90^{o}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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  $

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

$\tan \theta _B  =  \dfrac{ M _B}{M _A} \times \sqrt{3} $

$\tan \theta _B  \approx 0.7 $
$\theta  $ less than $45^o$

Multiple choice uniform magnetic field lines of earth magnetism physics

A deflection magnetometer is in Tan A position in a region where the Earth's horizontal component of magnetic induction is $60\times 10^{-6}T$. When a magnet is placed at a suitable distance, a deflection of $45^{0}$ is obtained. The induction field strength of the magnet is :

  1. $60\times 10^{-5}T $
  2. $6\times 10^{-5}T $
  3. $0.6\times 10^{-5}T $
  4. $6\times 10^{-6}T $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
In $\tan A$ position; magnetometer is set perpendicular to magnetic meridian
$B = B _4\tan\theta$                  [$B _4 = 60\times{10}^{-6}T, \theta=45°]$
$\Rightarrow B= 60\times{10}^{-6}\times \tan45°$
$\Rightarrow B = 6\times{10}^{-5}T.$
Hence, the answer is $6\times{10}^{-5}T.$