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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: Equipotential Surfaces

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Class 12

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

Topic: Equipotential Surfaces

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

Multiple Choice Questions

Q1. An equipotential surface is a surface on which:

  1. The electric field is constant
  2. The electric potential is constant
  3. The charge density is uniform
  4. The electric flux is maximum

Q2. The shape of equipotential surfaces due to a point charge is:

  1. Plane surfaces
  2. Concentric spheres
  3. Concentric cylinders
  4. Parallel lines

Q3. The work done in moving a charge along an equipotential surface is:

  1. Positive
  2. Negative
  3. Zero
  4. Depends on the path

Q4. Equipotential surfaces and electric field lines are:

  1. Parallel to each other
  2. At an angle of 45° to each other
  3. Perpendicular to each other
  4. Coincident with each other

Q5. The equipotential surfaces for a uniform electric field are:

  1. Concentric spheres
  2. Concentric cylinders
  3. Planes perpendicular to the field
  4. Planes parallel to the field

Q6. Two equipotential surfaces cannot intersect because:

  1. They would have different potentials at the point of intersection
  2. The electric field would have two directions at that point
  3. Both (a) and (b)
  4. They are always parallel

Short Answer Questions

Q7. Define equipotential surface. Why is no work done in moving a charge along an equipotential surface?

Q8. Draw the equipotential surfaces for (a) a point charge, and (b) a uniform electric field between two parallel plates.

Q9. Why are equipotential surfaces always perpendicular to electric field lines? Explain with a diagram.

Q10. A student draws two equipotential surfaces very close to each other around a point charge. What does this indicate about the electric field in that region?

Q11. The surface of a charged conductor is an equipotential surface. Explain why.

Q12. Can two different equipotential surfaces have the same potential? Justify your answer.

Long Answer Questions

Q13. Explain the properties of equipotential surfaces with suitable diagrams. Show that equipotential surfaces are always perpendicular to electric field lines and that no work is done in moving a charge along them.

Q14. Describe the equipotential surfaces for
(a) a single point charge,
(b) a uniform electric field, and
c) an electric dipole.
Draw rough sketches for each case and explain the spacing between the surfaces.

Q15. In a region of space, the electric potential is given by V = 4x + 3y, where V is in volts and x, y are in meters.

(a) Find the electric field in this region.

(b) What is the shape of the equipotential surfaces?

(c) Calculate the work done in moving a charge q = +2 μC from point (1 m, 2 m) to point (3 m, 4 m) along a path that lies on an equipotential surface.

Numerical / Application-Based Problems

Q16. A point charge Q = +10 μC is placed at the origin.

(a) Calculate the radius of the equipotential surface having a potential of 90 kV.

(b) Calculate the radius of the equipotential surface having a potential of 45 kV.

(c) Sketch roughly three equipotential surfaces around the charge, showing their relative spacing.

(d) A charge q = +1 μC is moved along the 90 kV equipotential surface from θ = 0° to θ = 180°. How much work is done by the electric field?

[Given: k = 9 × 10⁹ N m² C⁻²]

Q17. Two large parallel metal plates are separated by 5 cm and connected to a 50 V battery, creating a uniform electric field.

(a) Calculate the electric field between the plates.

(b) Draw at least three equipotential surfaces between the plates and label their potentials.

(c) A proton is moved from the positive plate to a point 2 cm from it along an equipotential surface. How much work is done?

(d) An electron is moved from the negative plate to the positive plate. Calculate the change in its potential energy.

[Given: e = 1.6 × 10⁻¹⁹ C]

Q18. The electric potential in a certain region is given by V = 5x² + 2y, where V is in volts and x, y are in meters.

(a) Find the electric field vector E at point (2 m, 1 m).

(b) Find the equation of the equipotential surface passing through point (2 m, 1 m).

(c) Calculate the work done by the electric field in moving a charge q = +3 μC from (2 m, 1 m) to (2 m, 3 m).

(d) Is the work done path-dependent or path-independent? Explain.


Total: 30 Marks | Time: 40 mins

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