Electric Potential due to a Point Charge: Formula and Examples

📚 Quick Study Guide

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• Electric Potential: Electric potential ($V$) at a point is the work done per unit charge to bring a test charge from infinity to that point.
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• Point Charge: A point charge is a charge that occupies a negligible amount of space.
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• Formula: The electric potential ($V$) due to a point charge ($q$) at a distance ($r$) is given by: $V = k \frac{q}{r}$, where $k$ is Coulomb's constant ($k \approx 8.99 \times 10^9 \text{ N m}^2/\text{C}^2$).
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• Units: Electric potential is measured in volts (V).
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• Sign Convention: The potential is positive for positive charges and negative for negative charges.
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• Potential at Infinity: Electric potential is usually defined to be zero at infinity.

Practice Quiz

1. Question 1: What is the electric potential due to a point charge of $+2 \text{ nC}$ at a distance of $3 \text{ m}$?
   1. A) $3 \text{ V}$
   2. B) $6 \text{ V}$
   3. C) $9 \text{ V}$
   4. D) $12 \text{ V}$
2. Question 2: If the electric potential at a point is $-18 \text{ V}$ due to a point charge at a distance of $1 \text{ m}$, what is the sign and approximate magnitude of the charge?
   1. A) $+2 \text{ nC}$
   2. B) $-2 \text{ nC}$
   3. C) $+6 \text{ nC}$
   4. D) $-6 \text{ nC}$
3. Question 3: How does the electric potential change with increasing distance from a positive point charge?
   1. A) Increases linearly
   2. B) Decreases linearly
   3. C) Increases inversely
   4. D) Decreases inversely
4. Question 4: What is the electric potential at infinity due to any point charge?
   1. A) Infinity
   2. B) Zero
   3. C) Depends on the charge
   4. D) 1 V
5. Question 5: Two point charges, $+q$ and $-q$, are placed close to each other. At a point equidistant from both charges, what is the electric potential?
   1. A) $k\frac{2q}{r}$
   2. B) Zero
   3. C) $k\frac{q}{r}$
   4. D) $-k\frac{2q}{r}$
6. Question 6: A charge of $+5 \text{ nC}$ creates an electric potential of $15 \text{ V}$ at a certain distance. What is that distance?
   1. A) $1 \text{ m}$
   2. B) $2 \text{ m}$
   3. C) $3 \text{ m}$
   4. D) $4 \text{ m}$
7. Question 7: Which of the following statements about electric potential due to a point charge is true?
   1. A) It is a vector quantity.
   2. B) It is directly proportional to the distance from the charge.
   3. C) It is inversely proportional to the distance from the charge.
   4. D) It is always positive.