The bob of a pendulum of mass m, suspended by | vedclass

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(C) The electric field $E$ produced by an infinite plane sheet of charge with surface charge density $\sigma$ is given by $E = \frac{\sigma}{2 \vareps

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$2 \pi \sqrt{\frac{L}{g-\frac{q \sigma}{2 \varepsilon_{0} m}}}$

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(C) The electric field $E$ produced by an infinite plane sheet of charge with surface charge density $\sigma$ is given by $E = \frac{\sigma}{2 \varepsilon_{0}}$.Since the bob carries a charge $q$, it experiences an upward electrostatic force $F_e = qE = \frac{q \sigma}{2 \varepsilon_{0}}$.The effective acceleration due to gravity $g_{	ext{eff}}$ acting on the bob is given by $m g_{	ext{eff}} = mg - F_e = mg - \frac{q \sigma}{2 \varepsilon_{0}}$.Thus, $g_{	ext{eff}} = g - \frac{q \sigma}{2 \varepsilon_{0} m}$.The time period $T$ of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{L}{g_{	ext{eff}}}}$.Substituting the value of $g_{	ext{eff}}$, we get $T = 2 \pi \sqrt{\frac{L}{g - \frac{q \sigma}{2 \varepsilon_{0} m}}}$.

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