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 ( (6d/7) ) + (E₀/K) ( (d/7) ) = E₀ d ( (6/7) + (1/7 × 4) ) . V = E₀ d ( (6/7) + (1/28) ) = E₀ d × (25/28) . C = (Q/V) = (Q/(25/28) V₀) = (28/25) × 250 = 280 pF . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d, 1/C_eq