The electric potential at a distance d from a point charge q in air of permittivity eo is expressed as?

Analyze the question: We need the formula for electric potential (V) at a distance d from a point charge q in a medium of permittivity ε₀.

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

Solution:

1. The electric field at distance r from 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 d: V = −∫(from ∞ to d) E dr = ∫(from d to ∞) q / (4πε₀r²) dr

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

4. Therefore: V = q / (4πε₀d)

Checking the options:

• A and B have q², which is wrong because potential is proportional to q, not q².
• C has d², which is the form for electric field, not potential.
• E has ε₀² and d, which is dimensionally wrong.
• D: q ÷ 4πε₀d matches our derived formula.

Tip: Remember the pair:

• Field: E = q / (4πε₀d²) (the d squared one)
• Potential: V = q / (4πε₀d) (just d)

Potential is "one power of d lower" than the field, since V is the integral of E over distance. Also, potential is a scalar and field is a vector.