A simple pendulum has bob mass m, positive charge q and length L. It is suspended above a large horizontal non-conducting sheet carrying uniform positive surface charge density σ.Assume qσ/(2ε₀m) < g.
The time period of small oscillations is:

Question

A simple pendulum has bob mass m, positive charge q and length L. It is suspended above a large horizontal non-conducting sheet carrying uniform positive surface charge density σ.Assume qσ/(2ε₀m) < g.

The time period of small oscillations is:

G1 Physics · Accepted Answer

The field of the sheet is E = σ/(2ε₀). The electric acceleration of the positive bob is upward: a e a_e a e ​ = qσ/(2ε₀m). Therefore, g e f f g_eff g e ​ f f = g - qσ/(2ε₀m). Hence, T = 2π√(L/ g e f f ) g_eff) g e ​ f f ) = 2π√{L/[g - qσ/(2ε₀m)]}.

A simple pendulum has bob mass m, positive charge q and length L. It is suspended above a large horizontal non-conducting sheet carrying uniform positive surface charge density σ.Assume qσ/(2ε₀m) &lt; g. The time period of small oscillations is:

A simple pendulum has bob mass m, positive charge q and length L. It is suspended above a large horizontal non-conducting sheet carrying uniform positive surface charge density σ.Assume qσ/(2ε₀m) < g. The time period of small oscillations is: