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.