Balanced Triangular Loop in Magnetic Field

Electricity and Magnetism Level 4

An equilateral triangular loop of mass \(M\) and side \(a\) at rest is under the influence of magnetic field B and gravitational field as shown in figure.

If the frame is slightly displaced in downward direction, the time period of small oscillations is given by

\(2\pi \sqrt{\dfrac{\sqrt{X}a}{Yg}}\)

Find \(X+Y\)

Details and assumptions

\(l = \frac{\sqrt{3}a}{4}\)

\(g\) is acceleration due to gravity


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