A uniform vertical electric field E is established in the space b… - Vidyadip

Question

A uniform vertical electric field $E$ is established in the space between two large parallel plates. A small conducting sphere of mass $m$ is suspended in the field from a string of length $L$. If the sphere is given $a + q$ charge and the lower plate is charged positvely, the period of oscillation of this pendulum is :-

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Answer

The equation of motion of sphere, $m a=m g-q E \Rightarrow a=g-\frac{q E}{m}$

Thus the effective acceleration of sphere oscillation will become$:$ $g^{\prime}=a=g-\frac{q E}{m}$

Time period, $T=2 \pi \sqrt{\frac{L}{g^{\prime}}}=2 \pi \sqrt{\frac{L}{g-\frac{q E}{m}}}$

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