The time period of vibrations of a dip needle in the vertical plane in the magnetic meridian is 3 s . When the same magnetic needle is made to vibrate in the horizontal plane, the time period is 3 2 s

Question

The time period of vibrations of a dip needle in the vertical plane in the magnetic meridian is 3 s . When the same magnetic needle is made to vibrate in the horizontal plane, the time period is 3 2 s . Then the angle of dip will be

TestHub · Accepted Answer

Time period of a dip needle vibration due to magnetic field is given by

$T = 2 π \sqrt{\frac{I}{M B}}$

In magnetic meridian $3 = 2 π \sqrt{\frac{I}{M B}}$ .......(1)

In horizontal plane, $3 \sqrt{2} = 2 π \sqrt{\frac{I}{M B_{H}}}$ .......(2)

$\frac{3}{3 \sqrt{2}} = \sqrt{\frac{B_{H}}{B}} = \sqrt{\frac{B \cos θ}{B}}$

$\cos θ = \frac{1}{2}$

Therefore angle of dip is $θ = 60^{o}$

Physics - Magnetism Question with Solution | TestHub

Options:

Doubts & Discussion