Question 24.94: Consider a particle with charge q = 1.50 × 10^-8 C, and take......
Consider a particle with charge q = 1.50 × 10^{-8} C, and take V = 0 at infinity. (a) What are the shape and dimensions of an equipotential surface having a potential of 30.0 V due to q alone? (b) Are surfaces whose potentials differ by a constant amount (1.0 V, say) evenly spaced?
(a) Using Eq. 24-26, we calculate the radius r of the sphere representing the 30 V equipotential surface:
V=\frac{1}{4 \pi \varepsilon_0} \frac{q}{r} (24-26)
r=\frac{q}{4 \pi \varepsilon_0 V}=\frac{\left(8.99 \times 10^9\, N \cdot m ^2 / C ^2\right)\left(1.50 \times 10^{-8} \,C \right)}{30\, V }=4.5\, m .
(b) If the potential were a linear function of r then it would have equally spaced equipotentials, but since V ∝ 1/r they are spaced more and more widely apart as r increases.