A 2.00 g air‑inflated balloon is given an excess negative charge, q 1 = − 3.75 × 10 − 8 C, by rubbing it with a blanket. It is found that a charged rod can be held above the balloon at a distance of d = 6.00 cm to make the balloon float. Assume the balloon and rod to be point charges. The Coulomb force constant is 1 / ( 4 π ϵ 0 ) = 8.99 × 10 9 N ⋅ m 2 / C 2 and the acceleration due to gravity is g = 9.81 m / s 2 .

(+2.093 × 10⁻⁷) C

Explanation:

Coulomb's law gives the force of attraction between two charges and it is given by

F = kq₁q₂/r²

where q₁ = charge on one of the two particles under consideration = charge on the balloon = - 3.75 × 10⁻⁸ C

q₂ = charge on the other body = charge on the rod = ?

k = Coulomb's constant = 1/(4 π ϵ₀) = 8.99 × 10⁹ N⋅m²/C²

r = distance between the two charges = d = 6.00 cm = 0.06 m

But for this question, the force of attraction between the charges was enough to lift the balloon and match its weight, Hence,

F = (kq₁q₂/d²) = - mg (negative because it's an attractive force)

m = mass of balloon = 2.00 g = 0.002 kg

g = acceleration due to gravity = 9.8 m/s²

(8.99 × 10⁹ × (-3.75 × 10⁻⁸) × q₂)/(0.06²) = 0.002 × 9.8

q₂ = (-0.002 × 9.8 × 0.06²)/(8.99 × 10⁹ × (-3.75 × 10⁻⁸)

q₂ = + 2.093 × 10⁻⁷ C

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.