AP Physics C E and M

Question

The potential of a 5.0 cm radius conducting sphere is -100 V. What is the charge density on its surface?

Group of answer choices

-1.8x10^-8 C/m²

3.5x10^-8 C/m²

2.2x10^-8 C/m²

-2.2x10^-8 C/m²

-3.5x10^-8 C/m²

Answer 1

Ans: -1.8x10^-8 C/m². The capacitance of a sphere of radius R, is C = 4πRε_o. ε_{o = Vacuum}  permittivity.   4πε_o = 1/(9x10⁹) Farad/meter. Here R = 5 cm = 0.05 m.

The total charge Q = CV. Here V= - 100 V. So, the total charge on the sphere is Q = -100 Vx0.05 m x (1/(9x10⁹)) Farad/meter = 5x10^-9/9 = 5.56x10^-10 C (Coulomb).

The surface density σ of charge is σ = Q/4πR² = 5.56x10^-10/(4π.(0.05)²) = 1.77x10^-8 C/m² ~ 1.8x10^-8 C/m²