First slide

Magnetic elements of Earth

Question

A dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period of vibration is found to be 2 second. The same needle is then allowed to vibrate in the horizontal plane and time period is again found to be 2 second. Then, the angle of dip is

Moderate

A

$0^{0}$
B

$30^{0}$
C

$45^{0}$
D

$90^{0}$

Solution

$T_{1} = 2 π \sqrt{\frac{I}{M B_{v}}} \to (1) T_{2} = 2 π \sqrt{\frac{I}{M B_{H}}} \to (2)$
$D i v i d i n g \frac{(2)}{(1)} = \frac{T_{2}}{T_{1}} = \sqrt{\frac{B_{v}}{B_{H}}} = \sqrt{\tan θ} [∴ B_{v} = B_{H} \tan θ] \Rightarrow \frac{2}{2} = \sqrt{\tan θ}$
$\Rightarrow \tan θ = 1 \Rightarrow θ = 45^{0}$

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