Question

answer the following questions about the charge distributions shown below: in fig. 24-28a, what is the potential at point p due to charge q at distance r from p? set v = 0 at infinity. express your answer in terms of given variables, ε₀ and π.

Explanation:

Step1: Recall the formula for electric potential due to a point charge

The electric potential \( V \) at a distance \( r \) from a point charge \( Q \) is given by the formula \( V=\frac{1}{4\pi\epsilon_0}\frac{Q}{r} \), where \( \epsilon_0 \) is the permittivity of free space, and we have set the potential at infinity (\( r \to \infty \)) to be zero.

Step2: Identify the values for \( Q \) and \( r \) in the problem

In this problem, the charge is \( Q \) and the distance from the charge \( Q \) to point \( P \) is \( R \). So we substitute \( r = R \) into the electric potential formula.

Substituting \( r = R \) into \( V=\frac{1}{4\pi\epsilon_0}\frac{Q}{r} \), we get \( V=\frac{1}{4\pi\epsilon_0}\frac{Q}{R} \).

Answer:

\(\frac{Q}{4\pi\epsilon_0 R}\)