A dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period of vibration is found to be 2 s . The same needle is then allowed to vibrate in the horizontal plane

Question

A dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period 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

TestHub · Accepted Answer

Time period when dip needle vibrates in the vertical plane perpendicular to the magnetic meridian is,

$T_{1} = 2 π \sqrt{\frac{I}{M B_{V}}}$

The time period of vibration when needle is allowed to vibrate in the horizontal plane is,

$T_{2} = 2 π \sqrt{\frac{I}{M B_{H}}}$

as $T_{1} = T_{2} = 2 s$

$∴ B_{V} = B_{H}$

Angle of dip is,

$\tan θ = \frac{B_{v}}{B_{H}} = 1$

$θ = 45 °$

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