# 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