Equilibrium of a Charged Body in a Uniform Electric Field

Equilibrium of a charged body in a uniform electric field occurs when the electric force on the charge exactly balances the gravitational force (weight) acting on it, resulting in zero net force.

Step 1: Identify the forces acting on the charged body

• Electric force (upward, along field direction): F_E = qE
• Gravitational force (downward): F_g = mg

Step 2: Apply the equilibrium condition

Step 3: Solve for charge

Step 4: Express charge in terms of excess electrons
If the body carries n excess electrons of charge e:

Step 5: For a spherical body of radius r and density ρ

Substituting into the equilibrium condition:

Given:

• Number of excess electrons, n = 12
• Electric field, E = 2.55 × 10⁴ N C⁻¹
• Oil density, ρ = 1.26 g cm⁻³ = 1260 kg m⁻³

Find: Radius r of the oil drop

Solution: Using

Rearranging for r:

Substituting values (e = 1.6 × 10⁻¹⁹ C, g = 9.8 m s⁻²):

Final Answer: r ≈ 9.8 × 10⁻⁷ m

Think of this like a hot air balloon held at a fixed height — buoyant force (upward) exactly cancels gravity (downward). Similarly, the electric force "buoys" the charged particle against gravity, holding it stationary in the field.