Tag: magnetism

Questions Related to magnetism

Two short magnets have equal pole strengths but one is twice as long as the other. The shorter magnet is placed $20\ cm$ in $\tan A$ position from the compass needle. The longer magnet must be placed on the other side of the magnetometer for no deflection at a distance equal to

uniform magnetic field lines of earth magnetism physics

  1. $20\ cm$

  2. $20\times (2)^{1/3} cm$

  3. $20\times (2)^{2/3} cm$

  4. $20\times (2)^{3/3} cm$

Show answer
Correct Option: B
Explanation:

For no deflection in $\tan A$ position
$\dfrac {\mu _{0}}{4\pi} \dfrac {2M _{1}}{d _{1}^{3}} \dfrac {2M _{2}}{d _{2}^{3}}$
$\therefore \dfrac {M _{1}}{M _{2}} = \left (\dfrac {d _{1}}{d _{2}}\right )^{3}$
or $\dfrac {1}{2} = \left (\dfrac {20}{d _{2}}\right )^{3}$
or $d _{2} = 20\times (2)^{1/3}cm$

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $2 sec$. The magnet is cut along its length into $3$ equal parts and the $3$ parts are then placed on each other with their like poles together. The time period of this combination will be

uniform magnetic field lines of earth magnetism physics

  1. $2 sec$

  2. $\dfrac{2}{9}sec$

  3. $2\sqrt{3}sec$

  4. $\dfrac{2}{\sqrt{3}}sec$

Show answer
Correct Option: B
Explanation:

$\dfrac{T _1}{T _2} =\sqrt{\frac{I _1}{I _2}} \sqrt{\dfrac{M _2}{M _1}}   ........(1)$
When the magnet is cut into three pieces, pole strength of the cut pieces is same as the original pole strength.
$I _1 =\dfrac{ml^2}{12}$
$I _2 = \dfrac{\dfrac{m}{3}(\dfrac{l}{3})^2}{12}$
$ \therefore = \dfrac{I _1}{I _2} = \dfrac{27}{1}$
$M _1 = pole \times l$ where pole is the pole strength.
$M _2= pole \times \dfrac{l}{3}$
$\dfrac{M _2}{M _1} = 3$
Eqn$(1)$  becomes
$\dfrac{T _1}{T _2}= \sqrt{\dfrac{27}{1}}\sqrt{3}=9$
Given $T _1=2$
$ \therefore T _2 = \dfrac{2}{9}$

With a standard rectangular bar magnet 'the time period of a vibration magnetometer is $4 s$. The bar magnet is cut parallel to its length into four equal pieces. The time period of vibration magnetometer when one piece is used (in second) (bar magnet breadth is, small) is

uniform magnetic field lines of earth magnetism physics

  1. $16$

  2. $8$

  3. $4$

  4. $2$

Show answer
Correct Option: C
Explanation:

Time period of magnet, $T=2\pi \sqrt { \dfrac { I }{ MB }  } $
When magnet is cut parallel to its length into four equal pieces.
Then new
magnetic moment, ${ M }^{ \prime  }=\dfrac { M }{ 4 } $
New moment of inertia, ${ I }^{ \prime  }=\dfrac { I }{ 4 } $
$\therefore $ New time period, ${ T }^{ \prime  }=2\pi \sqrt { \dfrac { { I }^{ \prime  } }{ { M }^{ \prime  }{ B }^{ \prime  } }  } $
$\Rightarrow \quad T={ T }^{ \prime  }=4s$