JEE Main - Electric potential and equipotential surfaces Online Test (MCQ Quiz)

1. What is the SI unit of electric potential?

A) Volt per meter B) Joule per Coulomb C) Ampere D) Farad

2. Electric potential is a scalar quantity. What does this imply?

A) It has both magnitude and direction. B) It only has magnitude. C) It is always positive. D) It is always negative.

3. Which of the following statements best describes electric potential?

A) The force experienced by a unit positive charge at a point. B) The work done in bringing a unit positive charge from infinity to that point against the electric field. C) The energy stored in an electric field. D) The rate of flow of electric charge.

4. An equipotential surface is a surface over which the electric potential is:

A) Constant B) Uniformly varying C) Zero D) Infinite

5. What is the relationship between electric field and equipotential surfaces?

A) The electric field is parallel to the equipotential surface. B) The electric field is perpendicular to the equipotential surface. C) The electric field is zero on an equipotential surface. D) The electric field is tangential to the equipotential surface.

6. In a region of uniform electric field, equipotential surfaces are:

A) Spherical B) Concentric spheres C) Parallel planes D) Cylindrical

7. For a single point charge, the equipotential surfaces are:

A) Parallel planes B) Cylinders C) Cones D) Concentric spheres

8. Work done in moving a charge between two points on the same equipotential surface is:

A) Maximum B) Minimum C) Zero D) Infinite

9. The electric potential at the center of a positively charged conducting sphere is:

A) Zero B) Negative C) Equal to the potential at the surface D) Greater than the potential at the surface

10. If the electric potential V is given by V = 6x - 8xy^2 + 2yz^2, what is the electric field at the origin (0,0,0)?

A) 6i - 8j + 0k B) 6i + 8j + 0k C) 0i + 0j + 0k D) 6i + 0j + 0k

11. Which of the following is a correct formula for electric potential (V) due to a point charge (q) at a distance (r)?

A) V = kq/r^2 B) V = kq^2/r C) V = kq/r D) V = k/qr

12. What is the potential difference between two points if 10 Joules of work is done to move a charge of 5 Coulombs between them?

A) 0.5 Volts B) 2 Volts C) 5 Volts D) 50 Volts

13. The electric potential inside a charged conductor is:

A) Uniform and non-zero B) Non-uniform and non-zero C) Uniform and equal to zero D) Uniform and equal to the potential at the surface

14. Electric field lines originate from positive charges and terminate on negative charges. Equipotential surfaces are:

A) Parallel to electric field lines. B) Perpendicular to electric field lines. C) Intersecting electric field lines at an angle of 45 degrees. D) Tangential to electric field lines.

15. If V(x,y,z) = x^2 + y^2 + z^2, what is the magnitude of the electric field at point (1, 2, 3)?

A) sqrt(14) B) 2 * sqrt(14) C) sqrt(56) D) 14

16. Consider two concentric spherical shells with charges +Q and -Q. The electric potential inside the inner shell is:

A) Zero B) Depends on the distance from the center C) Constant D) Negative

17. The potential energy of a system of two charges q1 and q2 separated by a distance r is given by:

A) k * q1 * q2 / r^2 B) k * q1 * q2 / r C) k * (q1 + q2) / r D) k * (q1 - q2) / r

18. What is the electric potential at infinity for a system of charges?

A) Always positive B) Always negative C) Always zero D) Depends on the charges

19. If the electric field is zero in a region, what can be said about the electric potential in that region?

A) It must be zero. B) It must be constant. C) It must be non-zero and constant. D) It can be anything.

20. Which of the following is NOT an equipotential surface for a uniformly charged infinite line?

A) Concentric cylinders B) Planes perpendicular to the line C) Cones with the line as axis D) None of the above

21. The electric potential at a point P due to a dipole depends on the distance r from the dipole and the angle theta between the dipole moment vector and the position vector as:

A) V proportional to 1/r B) V proportional to 1/r^2 C) V proportional to cos(theta)/r^2 D) V proportional to sin(theta)/r

22. What is the potential at the center of a square of side 'a' with charges q at each corner?

A) 4kq/a B) 2kq/a C) kq/a D) kq/(a * sqrt(2))

23. If the potential energy of a charge q at a point is U, the electric potential at that point is:

A) q/U B) U/q C) q*U D) U + q

24. For a dipole, the potential is zero on the:

A) Axial line B) Equatorial line C) Perpendicular bisector D) Both axial and equatorial lines

25. The work done to move a charge q from point A to point B is given by q(V_B - V_A). If A and B are on the same equipotential surface, then:

A) V_A > V_B B) V_A < V_B C) V_A = V_B D) V_A = -V_B

26. Consider two points A and B in an electric field. If V_A - V_B = 5V, and a charge of +2C is moved from A to B, the work done by the electric field is:

A) 10 J B) -10 J C) 2.5 J D) -2.5 J

27. What is the potential at the center of a uniformly charged ring of radius R and total charge Q?

A) KQ/R B) KQ/R^2 C) Zero D) K * Q * R

28. If the electric potential is given by V = A/r, then the electric field E is proportional to:

A) 1/r B) 1/r^2 C) 1/r^3 D) r^2

29. Which statement is correct regarding equipotential surfaces?

A) They can intersect each other. B) Electric field lines are parallel to them. C) Work done moving charge along them is zero. D) They are always spherical.

30. What is the potential difference between the center and the surface of a uniformly charged solid insulating sphere of radius R and charge Q?

A) KQ/(2R) B) KQ/R C) Zero D) 3KQ/(2R)

31. The electric potential due to an electric dipole at a point on its axis at a distance r from the center is proportional to:

A) 1/r B) 1/r^2 C) 1/r^3 D) r

32. If V is the electric potential and E is the electric field, which relation is correct?

A) E = -grad(V) B) V = -grad(E) C) E = grad(V) D) V = grad(E)

33. Two identical positive charges are placed at a separation. The electric potential midway between them is:

A) Zero B) Minimum C) Maximum D) Infinite

34. The electric potential at the surface of a positively charged conducting sphere is V. What is the potential at a point inside the sphere at a distance r from the center (r < R)?

A) V * (r/R) B) V * (R/r) C) V D) Zero

35. If a positive charge is moved from a region of low potential to a region of high potential, its potential energy:

A) Increases B) Decreases C) Remains the same D) Becomes zero

36. Which of the following represents the potential energy of a system of two point charges q1 and q2 separated by distance r?

A) k * q1 * q2 / r^2 B) k * (q1 + q2) / r C) k * q1 * q2 / r D) k * |q1 - q2| / r

37. In an electric field, equipotential lines are closer where the electric field is:

A) Weaker B) Stronger C) Uniform D) Zero

38. What is the electric potential at the center of a uniformly charged solid insulating sphere of radius R and charge Q?

A) KQ/R B) 3KQ/(2R) C) KQ/(2R) D) Zero

39. The potential difference between two points is 100V. If a charge of 1 microcoulomb is moved between these points, the work done is:

A) 100 Joules B) 10^-4 Joules C) 10^-6 Joules D) 10^8 Joules

40. If E = 2x^2 i + 3y^2 j + 4z^2 k, then the potential difference between the origin (0,0,0) and the point (1,1,1) is:

A) 10/3 V B) 3/10 V C) 3 V D) 10 V

41. What is the electric potential at a distance r from a point charge Q in vacuum?

A) Q / (4 * pi * epsilon_0 * r^2) B) Q / (4 * pi * epsilon_0 * r) C) Q^2 / (4 * pi * epsilon_0 * r) D) Q * r / (4 * pi * epsilon_0)

42. The equipotential surfaces corresponding to a dipole are:

A) Concentric spheres B) Parallel planes C) Complex shapes, not easily described D) Cylinders

43. Work done in moving a charge of -2 C from infinity to a point where the potential is 5V is:

A) 10 J B) -10 J C) 2.5 J D) -2.5 J

44. If the potential energy of a charge q at a point is U, the work done by the electric field in moving the charge from that point to infinity (where potential is zero) is:

A) U B) -U C) qU D) U/q

45. For a system of charges, the principle of superposition applies to:

A) Electric field only B) Electric potential only C) Both electric field and electric potential D) Neither electric field nor electric potential

46. What is the nature of equipotential surfaces for an isolated positive point charge?

A) Concentric spheres centered on the charge B) Parallel planes perpendicular to the electric field C) Cylinders coaxial with the charge D) Cones with vertex at the charge

47. If the electric field E = 0 everywhere, then the electric potential V must be:

A) Zero everywhere B) Constant everywhere C) Non-zero and constant everywhere D) Variable everywhere

48. Which statement is INCORRECT about equipotential surfaces?

A) Electric field is perpendicular to equipotential surfaces. B) Work done in moving a charge between any two points on an equipotential surface is zero. C) Equipotential surfaces can intersect each other. D) They are denser where the electric field is stronger.

49. The electric potential at a distance r from a uniformly charged infinite rod is proportional to:

A) 1/r B) 1/r^2 C) log(r) D) constant

50. What is the potential difference between two points separated by a distance of 1 meter in a uniform electric field of 100 N/C, if the displacement is along the field lines?

A) 100 V B) 0.01 V C) 1 V D) 0 V

Electric potential and equipotential surfaces - Online Test

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