Question:
A dip needle vibrates in a vertical plane perpendicular to magnetic meridian. The time of vibration is found to be $2 \,s$, the same needle is then allowed to vibrate in the horizontal plane and the time period is again found to be $2 \,s$. Then, the angle of dip is
A dip needle vibrates in a vertical plane perpendicular to magnetic meridian. The time of vibration is found to be $2 \,s$, the same needle is then allowed to vibrate in the horizontal plane and the time period is again found to be $2 \,s$. Then, the angle of dip is
Updated On: Jun 23, 2023
- $0^{\circ}$
- $30^{\circ}$
- $45^{\circ}$
- $90^{\circ}$
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The Correct Option is C
Solution and Explanation
Time of vibration is
$T=2\pi\sqrt{\frac{I}{MB}}$
In first case
$T_{1}=2\pi\sqrt{\frac{I}{MB_{V}}}$
In second case
$T_{2}=2\pi\sqrt{\frac{I}{MB_{H}}}$
Divide $\left(ii\right)$ by $\left(i\right)$, we get
$\therefore \frac{T_{2}}{T_{1}}=\sqrt{\frac{B_{V}}{B_{H}}}$
As $tan\,\delta=\frac{B_{V}}{B_{H}}$ where $\delta$ is the angle of dip
$\therefore \frac{T_{2}}{T_{1}}=\sqrt{tan\,\delta}$
As $T_{2}=T_{1}=2\,s$
$\therefore tan\delta=1$
$\delta=tan^{-1}\left(1\right)=45^{\circ}$
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Concepts Used:
Magnetism & Matter
Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.
Magnetite is the world’s first magnet. This is also called a natural magnet. Though magnets occur naturally, we can also impart magnetic properties to a substance. It would be an artificial magnet in that case.
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Some of the properties of the magnetic field lines are:
- The lines and continuous and outside the magnet, the field lines originate from the North pole and terminate at the South pole
- They form closed loops traversing inside the magnet.
- But here the lines seem to originate from the South pole and terminate at the North pole to form closed loops.
- More number of close lines indicate a stronger magnetic field
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- The tangent drawn at the field line gives the direction of the field at that point.