A simple pendulum of mass ' m ', length ' l ' and charge ' + q ' suspended in the…

A simple pendulum of mass ' m ', length ' l ' and charge '+q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be

  1. tan-1qmg×C1 V2-V1C1+C2(d-t)
  2. tan-1qmg×C2 V2-V1C1+C2(d-t)
  3. tan-1qmg×C2 V1+V2C1+C2(d-t)
  4. tan-1qmg×C1 V1+V2C1+C2(d-t)

Solution

Let E be electric field in air

Tsinθ=qE

Tcosθ=mg

tanθ=qEmg

Q=C1C2C1+C2V1+V2

E=QAϵo=C1C2C1+C2V1+V2Aϵo

C1=ϵ0 A d-tE=C2 V1+V2C1+C2(d-t)

Now θ=tan-1q·Emg

θ=tan-1qmg×C2 V1+V2C1+C2(d-t)

Asked in: JEE Main 2021 (27 Jul Shift 2)

Practice more Electrostatics questions on Aicharya