# Oscillations of a compass needle

Electricity and Magnetism Level 3

A small magnetic needle in a compass performs small oscillations about an axis perpendicular to the Earth's magnetic induction field. On a different Earth location it is observed that the needle's oscillation period decreased by $$\eta=1.5$$ times, that is $\frac{T_{location 1}}{T_{location 2}}= 1.5.$ How much did the magnetic field of the earth change? In other words, determine $x=\frac{B_{location 2}}{B_{location 1}}.$ You may neglect the Earth's gravitational field in this problem.

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