Practice question

**Spherical conductor capacitance** C = 4π ε₀ R, R radius (m), potential V = Q/C = Q/(4π ε₀ R)=k Q/R. For R=2 cm=0.02 m, Q=2×10⁻⁸ C, V=9×10⁹×2×10⁻⁸/0.02=9000 V, showing high voltage for small sphere with modest charge. Potential difference: V = E₀ ( (d/2) ) + (E₀/K) ( (d/2) ) = E₀ d ( (1/2) + (1/2 × 4) ) = E₀ d ( (1/2) + (1/8) ) = (5/8) E₀ d . C = (Q/V) = (Q/(5/8) V₀) = (8/5) × (Q/V₀) = (8/5) × 10 = 16 pF . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d,