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Class 12  »  Physics  »  Electrostatic Potential and Capacitance

Potential due to Point Charge Dipole System of Charges - UNSOLVED PRACTICE SET

Class 12

Chapter: Electrostatic Potential and Capacitance | Topic: Potential due to Point Charge Dipole System of Charges

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Class 12

POTENTIAL DUE TO POINT CHARGE DIPOLE SYSTEM OF CHARGES - UNSOLVED PRACTICE SET

Topic: Potential due to Point Charge Dipole System of Charges

Time: 40 mins | Marks: 30 | Difficulty: Medium

Multiple Choice Questions

Q1. The electric potential at a distance r from a point charge Q is given by:

  1. kQ/r²
  2. kQ/r
  3. kQr
  4. kQ²/r

Q2. The electric potential on the perpendicular bisector of an electric dipole is:

  1. Maximum
  2. Zero
  3. Negative
  4. Infinite

Q3. For a system of charges, the total electric potential at a point is:

  1. The vector sum of potentials due to individual charges
  2. The scalar sum of potentials due to individual charges
  3. The product of individual potentials
  4. The difference between the maximum and minimum potentials

Q4. The electric potential at the center of a square with charges +q, +q, −q, and −q at its corners is:

  1. 4kq/a
  2. Zero
  3. 2kq/a
  4. kq/a

Q5. The potential due to an electric dipole at a point on its axial line varies as:

  1. 1/r
  2. 1/r²
  3. 1/r³
  4. r

Q6. Two point charges +q and −q are placed at a distance 2a apart. The potential at the midpoint between them is:

  1. kq/a
  2. −kq/a
  3. Zero
  4. 2kq/a

Short Answer Questions

Q7. Write the expression for electric potential due to a point charge. How does it differ from the expression for electric field due to a point charge?

Q8. Derive the expression for electric potential at a point on the axial line of an electric dipole.

Q9. Why is the electric potential at any point on the equatorial line of a dipole zero? Explain with reasoning.

Q10. Three charges +q, +q, and −2q are placed at the vertices of an equilateral triangle. What is the electric potential at the centroid of the triangle?

Q11. A student places two charges +5 μC and −5 μC 10 cm apart. Calculate the electric potential at a point 10 cm from each charge (forming an equilateral triangle).

Q12. How does the electric potential due to a dipole differ from that due to a single point charge in terms of distance dependence?

Long Answer Questions

Q13. Derive an expression for the electric potential at any point due to an electric dipole. Show that on the axial line, V = kp/r², and on the equatorial line, V = 0.

Q14. Four charges +q, +q, −q, and −q are placed at the four corners of a square of side 'a'. Find the electric potential at the center of the square. What would be the potential if all four charges were +q?

Q15. Three point charges q₁ = +2 μC, q₂ = −4 μC, and q₃ = +6 μC are placed at the vertices of an equilateral triangle of side 30 cm.

(a) Calculate the electric potential at the centroid of the triangle.

(b) Calculate the electric potential at the midpoint of the side joining q₁ and q₂.

(c) How much work is required to bring a charge q = +1 μC from infinity to the centroid?

[Given: k = 9 × 10⁹ N m² C⁻²]

Numerical / Application-Based Problems

Q16. An electric dipole consists of charges ±3 μC separated by a distance of 4 cm.

(a) Calculate the dipole moment.

(b) Find the electric potential at a point on the axial line, 20 cm from the center of the dipole.

(c) Find the electric potential at a point on the equatorial line, 20 cm from the center.

(d) Calculate the work done in moving a charge q = +0.5 μC from the equatorial point to the axial point.

[Given: k = 9 × 10⁹ N m² C⁻²]

Q17. In a classroom demonstration, a teacher arranges four identical charges q = +2 μC at the four corners of a square of side 40 cm.

(a) Calculate the electric potential at the center of the square.

(b) A fifth charge Q = −1 μC is brought from infinity to the center. How much work is done?

(c) If one of the corner charges is replaced by −2 μC, what is the new potential at the center?

(d) A student argues that the electric field at the center is zero in case (a) but not in case (c). Is the student correct? Explain.

[Given: k = 9 × 10⁹ N m² C⁻²]

Q18. A system consists of two charges: q₁ = +8 μC at the origin and q₂ = −2 μC at x = 30 cm on the x-axis.

(a) Find the point(s) on the x-axis where the electric potential is zero.

(b) Find the point(s) on the x-axis where the electric field is zero.

(c) Is there any point on the y-axis where the electric potential is zero? Explain.

(d) Calculate the potential at a point P on the y-axis at y = 40 cm.

[Given: k = 9 × 10⁹ N m² C⁻²]


Total: 30 Marks | Time: 40 mins

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