A charged pendulum of mass m, charge q and length L is near a large positively charged sheet of surface charge density σ. The sheet is tilted so that its plane makes angle β with the horizontal.Let electric acceleration is $a_e$ = qσ/(2ε₀m).The time period of small oscillations about the new equilibrium position is:
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Question

A charged pendulum of mass m, charge q and length L is near a large positively charged sheet of surface charge density σ. The sheet is tilted so that its plane makes angle β with the horizontal.Let electric acceleration is $a_e$ = qσ/(2ε₀m).The time period of small oscillations about the new equilibrium position is:

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G1 Physics · Accepted Answer

The electric acceleration has magnitude a e a_e a e ​ = qσ/(2ε₀m) and is normal to the sheet. The magnitude of the effective constant acceleration is g e f f g_eff g e ​ f f = √(g²+ a e 2 − 2 g a e a_e²-2ga_e a e 2 ​ − 2 g a e ​ cosβ). Therefore, T = 2π√(L/ g e f f ) g_eff) g e ​ f f ) = 2π√{L/√(g²+ a e 2 − 2 g a e a_e²-2ga_e a e 2 ​ − 2 g a e ​ cosβ)}.