As shown in the figure, a particle P carries a charge of -0.01 C and has a mass of 10 mg . Each capacitor plate possesses a one-sided surface area of 100 cm ^2 . Determine the potential difference V that must be applied across the combination to maintain the particle P in equilibrium.

Step-by-step solution

For the particle to be in equilibrium, the upward electric force must balance the downward gravitational force: |q|E = mg Since the two identical capacitors are connected in series, the potential difference across each capacitor is V' = V 2 . The electric field between the plates of the top capacitor is E = V' d = V 2d . Substituting this into the equilibrium equation: |q| V 2d = mg V = 2dmg |q| The capacitance of a parallel plate capacitor is C = ₀ A d , which gives d = ₀ A C . Substituting d into the expression f