The correct expression for the potential at a point distance r from a charge q in an electric field is?

Analyze the question: You are asked for the electric potential V at a distance r from a point charge q.

Concept: Electric potential is the work done per unit charge in bringing a small positive test charge from infinity to that point. It is a scalar quantity.

Solution:

1. The electric field of a point charge is E = q / (4πε₀r²)

2. Potential is the work done per unit charge against this field, brought in from infinity to distance r: V = −∫ from ∞ to r of E dr = ∫ from r to ∞ of q / (4πε₀r²) dr

3. Integrating: V = (q / 4πε₀) · [−1/r] from r to ∞ = (q / 4πε₀) · (1/r)

V = q / (4πε₀r)

Checking the options:

• A and B: these show q² in the numerator (the "_q2" looks like a formatting glitch), which is wrong. Potential is linear in q.
• C: q / (4πε₀r²) is the electric field strength E, not the potential.
• D: q / (4πε₀r) is the correct expression for potential. ✔

Tip: Remember the pair:

• Field: E = kq/r², with r squared
• Potential: V = kq/r, with r to the first power

Also, V = E × r, which is why one power of r disappears. Here k = 1/(4πε₀).