Question

A bar magnet is freely suspended in such a way that

Answer 1

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a bar magnet is freely suspended in such a way that when it oscillates in the horizontal plane it makes 20 oscillations per minute at a place where dip angle is 30 degree and 15 oscillations per minute at a place where dip angle is 60 degree.

Answer 2

The ratio of total earth magnetic field at the two places is 3.0.

Explanation:

Suppose that it oscillates in the horizontal plane .it makes 20 oscillations per minute at a place where dip angle is 30 and 15 oscillations per minute at a place where dip angle is 60. The ratio of total earth magnetic field at the two places is

We need to calculate the number of oscillation

Using formula of number of oscillation

$n=\dfrac{1}{2\pi}\sqrt{\dfrac{B\sin\theta}{I}}$

Put the value into the formula

For 20 oscillations,

$20=\dfrac{1}{2\pi}\sqrt{\dfrac{B\sin30}{I}}$...(I)

For 15 oscillations,

$15=\dfrac{1}{2\pi}\sqrt{\dfrac{B'\sin60}{I}}$...(II)

We need to calculate the ratio of total earth magnetic field at the two places

Divided equation (I) by equation (II)

$\dfrac{20}{15}=\dfrac{\sqrt{\dfrac{B\sin30}{I}}}{\sqrt{\dfrac{B'\sin60}{I}}}$

$\dfrac{20^2}{15^2}=\dfrac{B\times\dfrac{1}{2}}{B'\times\dfrac{\sqrt{3}}{2}}$

$\dfrac{B}{B'}=\dfrac{20^2\times\sqrt{3}}{15^2}$

$\dfrac{B}{B'}=3.0$

Hence, The ratio of total earth magnetic field at the two places is 3.0.

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