Charged Pendulum!

A charged particle having its charge to mass ratio as \(\beta\) goes in a conical pendulum of length \(L\) making an angle \(\theta\) with vertical and angular velocity \(\omega\). If a magnetic field \(B\) is directed vertically downwards (see figure), then:

\((A) B = \frac{1}{\beta}[\omega - \frac{g}{\omega L \cos \theta}]\)

\((B)\) Angular momentum of the particle about the point of suspension remains constant .

\((C)\) If the direction of \(B\) were reversed maintaining same \(\omega\) and \(L\), then \(\theta\) will remain unchanged.

\((D)\) Rate of change of angular momentum of the particle about the point of suspension is not a constant vector.

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