⚡ ELECTRIC POTENTIAL, POTENTIAL ENERGY, POTENTIAL DIFFERENCE CONCEPTS, V DUE TO A POINT CHARGE. QUIZ1

🧠 Section A: Theory & Conceptual Questions (1–10)

Q1. Define electric potential at a point. Is it a scalar or vector quantity?

Q2. What is the physical meaning of potential difference between two points?

Q3. Can electric potential be zero at a point where electric field is non-zero? Explain.

Q4. Write the expression for electric potential due to a point charge. What happens when distance increases?

Q5. Define electric potential energy of a system of two charges.

Q6. Why is electric potential constant inside a conductor in electrostatic equilibrium?

Q7. What is the relation between electric field and potential?

Q8. If a positive charge is moved against an electric field, what happens to its potential energy?

Q9. What is equipotential surface? Give one important property.

Q10. Why do two equipotential surfaces never intersect?

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🔢 Section B: Numerical Problems (11–20)

Q11. Calculate the electric potential at a point 2 m away from a charge of $5 \times 10^{-6}\,C$.
(Given: $k = 9 \times 10^9$)

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Q12. Find the potential difference between two points at distances 2 m and 5 m from a charge $2 \times 10^{-6}\,C$.

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Q13. Two charges $+2\mu C$ and $+3\mu C$ are placed 4 m apart. Find the electric potential energy of the system.

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Q14. A charge of $1\mu C$ is brought from infinity to a point where potential is 5 V. Find the work done.

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Q15. Find the electric potential at a point due to two charges $+2\mu C$ and $-1\mu C$ placed 3 m and 4 m away respectively.

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Q16. Calculate the distance from a charge $4 \times 10^{-6}\,C$ where the potential is 18,000 V.

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Q17. A charge $2C$ is moved through a potential difference of 10 V. Calculate the work done.

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Q18. Find the potential at the midpoint between two equal charges $+4\mu C$ separated by 2 m.

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Q19. Calculate the potential energy of three charges placed at the corners of an equilateral triangle (side = 1 m), each charge $1\mu C$.

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Q20. If the electric field is $5\,N/C$, find the potential difference across 2 m distance along the field.

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✅ ANSWER KEY

Section A (Conceptual)

1. Work done per unit charge; scalar
2. Work done per unit charge between two points
3. Yes (example: inside conductor)
4. $V = \frac{kq}{r}$, decreases with distance
5. Work done in assembling charges
6. Charges rearrange to cancel internal field
7. $E = -\frac{dV}{dr}$
8. Potential energy increases
9. Surface of constant potential; no work done
10. Unique potential at a point

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Section B (Final Answers)

Q11. $22500\,V$

Q12. $5400\,V$

Q13. $13.5 \times 10^{-3}\,J$

Q14. $5 \times 10^{-6}\,J$

Q15. $6000 - 2250 = 3750\,V$

Q16. $2\,m$

Q17. $20\,J$

Q18. $72000\,V$

Q19. $0.027\,J$

Q20. $10\,V$

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🧾 DETAILED SOLUTIONS

Q11

$$V = \frac{kq}{r} = \frac{9 \times 10^9 \times 5 \times 10^{-6}}{2} = 22500\,V$$

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Q13

$$U = \frac{k q_1 q_2}{r} = \frac{9 \times 10^9 \times 2 \times 10^{-6} \times 3 \times 10^{-6}}{4} = 13.5 \times 10^{-3}\,J$$

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Q14

$$W = qV = 1 \times 10^{-6} \times 5 = 5 \times 10^{-6}\,J$$

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Q16

$$r = \frac{kq}{V} = \frac{9 \times 10^9 \times 4 \times 10^{-6}}{18000} = 2\,m$$

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Q17

$$W = qV = 2 \times 10 = 20\,J$$

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Q19

Total energy = sum of all pairs:

$$U = 3 \times \frac{kq^2}{r} = 3 \times \frac{9 \times 10^9 \times (10^{-6})^2}{1} = 0.027\,J$$

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Q20

$$V = E \cdot d = 5 \times 2 = 10\,V$$