Question

For a dipole with \[p = 3 \times 10^{-10}\ \text{C}\cdot\text{m}\], \[l = 0.05\ \text{m}\], evaluated at an axial point \[r = 0.2\ \text{m}\] using \[k = 9 \times 10^9\ \text{N}\cdot\text{m}^2/\text{C}^2\] in the formula \[V = \frac{kp}{r^2 - l^2}\], the potential is:

Options

• 27 volts

• 72 volts

• 135 volts

• 7.2 volts

Answer 1

V = kp/(r² − l²) = (9 × 10⁹ × 3 × 10⁻¹⁰)/((0.2)² − (0.05)²) = 2.7/0.0375 = 72 volts. The denominator uses the exact axial expression r² − l² rather than just r².