Electrostatics

What is Electrostatics?

Electrostatics is a fundamental chapter in Physics that focuses on the study of stationary electric charges and their interactions. This chapter introduces students to the basic principles of electric forces, fields, and potentials, providing a comprehensive understanding of how electric charges interact when at rest. The unit covers the concepts of Coulomb’s Law, which describes the force between two point charges, and explores the electric field and electric potential associated with these charges. It also delves into the properties of conductors and insulators, and the principles of electric shielding.

Key Topics in Electrostatics:

• Coulomb’s Law: Understanding the force between two charges, including the inverse-square law and its mathematical representation.
• Electric Field: Analyzing the concept of electric fields generated by point charges and continuous charge distributions.
• Electric Potential: Learning about electric potential energy and potential difference, and how to calculate the work done in moving a charge within an electric field.
• Capacitance: Exploring capacitors and their role in storing electrical energy, including the calculation of capacitance and energy stored in capacitors.
• Gauss’s Law: Applying Gauss’s Law to determine electric fields in symmetric charge distributions and understanding its significance in electrostatics.

Benefits of Studying Electrostatics:

• Foundation for Advanced Topics: Provides a crucial basis for understanding more complex electrical phenomena and circuits in advanced Physics and Engineering courses.
• Practical Applications: Offers insights into real-world applications such as capacitors in electronic devices, electrostatic precipitators in pollution control, and the behavior of materials in electric fields.
• Academic Success: Equips students with a strong grasp of fundamental concepts that are essential for solving problems in electrostatics and preparing for higher-level Physics exams.

This chapter is vital for understanding the principles of electric charges and fields, which are foundational to many areas of Physics and practical technologies. Mastering Electrostatics is essential for academic success and for applying these concepts in real-world scenarios.

1. The unit of electric charge is:

a) Ampere (A)
b) Volt (V)
c) Coulomb (C)
d) Ohm (Ω)
Answer: c) Coulomb (C)

2. The force between two charges is given by:

a) Coulomb’s Law
b) Ohm’s Law
c) Newton’s Law
d) Faraday’s Law
Answer: a) Coulomb’s Law

3. Coulomb’s Law states that the force between two point charges is:

a) Inversely proportional to the square of the distance between them
b) Directly proportional to the product of their charges
c) Independent of the distance between them
d) Both a) and b)
Answer: d) Both a) and b)

4. The electric field intensity (E) at a point due to a positive point charge is given by:

a) E=kQr2E = \frac{kQ}{r^2}E=r2kQ​
b) E=Q4πϵ0r2E = \frac{Q}{4\pi \epsilon_0 r^2}E=4πϵ0​r2Q​
c) E=FQE = \frac{F}{Q}E=QF​
d) E=kQE = \frac{k}{Q}E=Qk​
Answer: b) E=Q4πϵ0r2E = \frac{Q}{4\pi \epsilon_0 r^2}E=4πϵ0​r2Q​

5. The unit of electric field intensity is:

a) Newton per Coulomb (N/C)
b) Coulomb per Newton (C/N)
c) Joule per Coulomb (J/C)
d) Volt per meter (V/m)
Answer: a) Newton per Coulomb (N/C)

6. The electric potential at a point is defined as:

a) Work done per unit charge in bringing a positive test charge from infinity to that point
b) Force experienced by a unit charge at that point
c) Energy stored per unit volume at that point
d) Charge per unit area at that point
Answer: a) Work done per unit charge in bringing a positive test charge from infinity to that point

7. The unit of electric potential is:

a) Volt (V)
b) Ampere (A)
c) Coulomb (C)
d) Ohm (Ω)
Answer: a) Volt (V)

8. The electric potential due to a point charge (Q) at a distance (r) is given by:

a) V=kQrV = \frac{kQ}{r}V=rkQ​
b) V=Q4πϵ0rV = \frac{Q}{4\pi \epsilon_0 r}V=4πϵ0​rQ​
c) V=Qr2V = \frac{Q}{r^2}V=r2Q​
d) V=krV = \frac{k}{r}V=rk​
Answer: b) V=Q4πϵ0rV = \frac{Q}{4\pi \epsilon_0 r}V=4πϵ0​rQ​

9. The relationship between electric field (E) and electric potential (V) is:

a) E=−dVdrE = -\frac{dV}{dr}E=−drdV​
b) E=dVdrE = \frac{dV}{dr}E=drdV​
c) E=VrE = \frac{V}{r}E=rV​
d) E=−VrE = -\frac{V}{r}E=−rV​
Answer: a) E=−dVdrE = -\frac{dV}{dr}E=−drdV​

10. The work done (W) in moving a charge (Q) through an electric potential difference (V) is given by:

a) W=QVW = QVW=QV
b) W=QVrW = \frac{QV}{r}W=rQV​
c) W=VQW = \frac{V}{Q}W=QV​
d) W=QVW = \frac{Q}{V}W=VQ​
Answer: a) W=QVW = QVW=QV

11. The capacitance (C) of a capacitor is defined as:

a) The charge stored per unit potential difference
b) The potential difference per unit charge
c) The work done per unit charge
d) The energy stored per unit charge
Answer: a) The charge stored per unit potential difference

12. The unit of capacitance is:

a) Farad (F)
b) Volt (V)
c) Ampere (A)
d) Coulomb (C)
Answer: a) Farad (F)

13. The capacitance of a parallel plate capacitor is given by:

a) C=ϵ0AdC = \frac{\epsilon_0 A}{d}C=dϵ0​A​
b) C=dϵ0AC = \frac{d}{\epsilon_0 A}C=ϵ0​Ad​
c) C=Aϵ0dC = \frac{A}{\epsilon_0 d}C=ϵ0​dA​
d) C=ϵ0dAC = \frac{\epsilon_0 d}{A}C=Aϵ0​d​
Answer: a) C=ϵ0AdC = \frac{\epsilon_0 A}{d}C=dϵ0​A​

14. The energy (E) stored in a capacitor is given by:

a) E=12CV2E = \frac{1}{2} CV^2E=21​CV2
b) E=12QVE = \frac{1}{2} QVE=21​QV
c) E=12Q2CE = \frac{1}{2} \frac{Q^2}{C}E=21​CQ2​
d) All of the above
Answer: d) All of the above

15. When capacitors are connected in series, the equivalent capacitance (C_eq) is given by:

a) 1Ceq=1C1+1C2+⋯+1Cn\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n}Ceq​1​=C1​1​+C2​1​+⋯+Cn​1​
b) Ceq=C1+C2+⋯+CnC_{eq} = C_1 + C_2 + \cdots + C_nCeq​=C1​+C2​+⋯+Cn​
c) Ceq=C1C2C1+C2C_{eq} = \frac{C_1 C_2}{C_1 + C_2}Ceq​=C1​+C2​C1​C2​​
d) Ceq=C1+C2C1C2C_{eq} = \frac{C_1 + C_2}{C_1 C_2}Ceq​=C1​C2​C1​+C2​​
Answer: a) 1Ceq=1C1+1C2+⋯+1Cn\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n}Ceq​1​=C1​1​+C2​1​+⋯+Cn​1​

16. When capacitors are connected in parallel, the equivalent capacitance (C_eq) is given by:

a) Ceq=C1+C2+⋯+CnC_{eq} = C_1 + C_2 + \cdots + C_nCeq​=C1​+C2​+⋯+Cn​
b) 1Ceq=1C1+1C2+⋯+1Cn\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n}Ceq​1​=C1​1​+C2​1​+⋯+Cn​1​
c) Ceq=C1C2C1+C2C_{eq} = \frac{C_1 C_2}{C_1 + C_2}Ceq​=C1​+C2​C1​C2​​
d) Ceq=C1+C2C1C2C_{eq} = \frac{C_1 + C_2}{C_1 C_2}Ceq​=C1​C2​C1​+C2​​
Answer: a) Ceq=C1+C2+⋯+CnC_{eq} = C_1 + C_2 + \cdots + C_nCeq​=C1​+C2​+⋯+Cn​

17. The electric potential energy (U) of a system of charges is given by:

a) U=14πϵ0∑qiqjrijU = \frac{1}{4\pi \epsilon_0} \sum \frac{q_i q_j}{r_{ij}}U=4πϵ0​1​∑rij​qi​qj​​
b) U=12QVU = \frac{1}{2} QVU=21​QV
c) U=12CV2U = \frac{1}{2} CV^2U=21​CV2
d) U=14πϵ0∑qiqjrij2U = \frac{1}{4\pi \epsilon_0} \sum \frac{q_i q_j}{r_{ij}^2}U=4πϵ0​1​∑rij2​qi​qj​​
Answer: a) U=14πϵ0∑qiqjrijU = \frac{1}{4\pi \epsilon_0} \sum \frac{q_i q_j}{r_{ij}}U=4πϵ0​1​∑rij​qi​qj​​

18. The electric flux through a closed surface is given by:

a) Φ=Qencϵ0\Phi = \frac{Q_{enc}}{\epsilon_0}Φ=ϵ0​Qenc​​
b) Φ=E⋅A\Phi = E \cdot AΦ=E⋅A
c) Φ=E⋅Aϵ0\Phi = \frac{E \cdot A}{\epsilon_0}Φ=ϵ0​E⋅A​
d) Φ=Qenc⋅Aϵ0\Phi = \frac{Q_{enc} \cdot A}{\epsilon_0}Φ=ϵ0​Qenc​⋅A​
Answer: a) Φ=Qencϵ0\Phi = \frac{Q_{enc}}{\epsilon_0}Φ=ϵ0​Qenc​​

19. Gauss’s Law states that the total electric flux through a closed surface is proportional to:

a) The electric field intensity at the surface
b) The surface area of the closed surface
c) The charge enclosed within the surface
d) The potential difference across the surface
Answer: c) The charge enclosed within the surface

20. The electric field inside a charged conductor in electrostatic equilibrium is:

a) Zero
b) Maximum at the surface
c) Constant throughout
d) Increasing towards the center
Answer: a) Zero

21. The potential difference between two points in an electric field is:

a) The work done in moving a unit positive charge from one point to another
b) The force experienced by a unit positive charge
c) The product of the charge and the distance
d) The work done in moving a unit charge from infinity to one point
Answer: a) The work done in moving a unit positive charge from one point to another

22. The electric field due to a uniformly charged infinite plane sheet is:

a) σ2ϵ0\frac{\sigma}{2\epsilon_0}2ϵ0​σ​
b) σ4πϵ0\frac{\sigma}{4\pi \epsilon_0}4πϵ0​σ​
c) σϵ0\frac{\sigma}{\epsilon_0}ϵ0​σ​
d) Q4πϵ0r2\frac{Q}{4\pi \epsilon_0 r^2}4πϵ0​r2Q​
Answer: c) σϵ0\frac{\sigma}{\epsilon_0}ϵ0​σ​

23. The potential due to an infinite line of charge is:

a) λ2πϵ0ln⁡r\frac{\lambda}{2 \pi \epsilon_0} \ln r2πϵ0​λ​lnr
b) λ4πϵ0r\frac{\lambda}{4 \pi \epsilon_0 r}4πϵ0​rλ​
c) λ4πϵ0r2\frac{\lambda}{4 \pi \epsilon_0 r^2}4πϵ0​r2λ​
d) λr4πϵ0\frac{\lambda r}{4 \pi \epsilon_0}4πϵ0​λr​
Answer: a) λ2πϵ0ln⁡r\frac{\lambda}{2 \pi \epsilon_0} \ln r2πϵ0​λ​lnr

24. In a conductor, the electric field is:

a) Parallel to the surface
b) Perpendicular to the surface
c) Zero everywhere
d) Always directed towards the center
Answer: b) Perpendicular to the surface

25. The capacitance of a spherical capacitor with inner radius r1r_1r1​ and outer radius r2r_2r2​ is given by:

a) C=4πϵ0r1r2r2−r1C = 4\pi \epsilon_0 \frac{r_1 r_2}{r_2 – r_1}C=4πϵ0​r2​−r1​r1​r2​​
b) C=4πϵ0r2−r1r1r2C = 4\pi \epsilon_0 \frac{r_2 – r_1}{r_1 r_2}C=4πϵ0​r1​r2​r2​−r1​​
c) C=4πϵ0r1r2r1+r2C = 4\pi \epsilon_0 \frac{r_1 r_2}{r_1 + r_2}C=4πϵ0​r1​+r2​r1​r2​​
d) C=4πϵ0(r2−r1)C = 4\pi \epsilon_0 (r_2 – r_1)C=4πϵ0​(r2​−r1​)
Answer: a) C=4πϵ0r1r2r2−r1C = 4\pi \epsilon_0 \frac{r_1 r_2}{r_2 – r_1}C=4πϵ0​r2​−r1​r1​r2​​

26. The energy stored in a capacitor is:

a) U=12CV2U = \frac{1}{2} CV^2U=21​CV2
b) U=QVU = QVU=QV
c) U=12Q2/CU = \frac{1}{2} Q^2/CU=21​Q2/C
d) All of the above
Answer: d) All of the above

27. The electric field inside a charged hollow sphere is:

a) Zero
b) Equal to the field outside the sphere
c) Maximum at the center
d) Varies inversely with the distance from the center
Answer: a) Zero

28. For a capacitor, the relation between charge (Q), capacitance (C), and potential difference (V) is:

a) Q=CVQ = CVQ=CV
b) V=QCV = \frac{Q}{C}V=CQ​
c) C=QVC = \frac{Q}{V}C=VQ​
d) All of the above
Answer: d) All of the above

29. The electrostatic force between two charges is:

a) Always attractive
b) Always repulsive
c) Depends on the medium between them
d) Always zero
Answer: c) Depends on the medium between them

30. The electric field due to a point charge is:

a) Uniform
b) Radially outward or inward
c) Constant in magnitude
d) Zero at all points
Answer: b) Radially outward or inward

31. The electric field lines:

a) Always start from positive charges and end on negative charges
b) Always form closed loops
c) Are always parallel to each other
d) Can cross each other
Answer: a) Always start from positive charges and end on negative charges

32. The force between two charges is inversely proportional to:

a) The product of the charges
b) The distance between the charges
c) The square of the distance between the charges
d) The cube of the distance between the charges
Answer: c) The square of the distance between the charges

33. The dielectric constant of a material is:

a) The ratio of the electric field without dielectric to the electric field with dielectric
b) The ratio of the capacitance with dielectric to the capacitance without dielectric
c) The ratio of the charge with dielectric to the charge without dielectric
d) The ratio of the energy stored with dielectric to the energy stored without dielectric
Answer: b) The ratio of the capacitance with dielectric to the capacitance without dielectric

34. The electric potential at a point in an electric field is:

a) The work done in moving a positive charge from infinity to that point
b) The potential energy per unit charge at that point
c) The force per unit charge at that point
d) The work done per unit charge in moving a charge between two points
Answer: b) The potential energy per unit charge at that point

35. The electric field due to a dipole decreases as:

a) The square of the distance from the dipole
b) The cube of the distance from the dipole
c) The fourth power of the distance from the dipole
d) The distance from the dipole
Answer: b) The cube of the distance from the dipole

36. The work done to bring a charge from infinity to a point in an electric field is equal to:

a) The electric potential at that point
b) The potential energy at that point
c) The electric field intensity at that point
d) The electric flux through a surface enclosing that point
Answer: b) The potential energy at that point

37. The electric field inside a conductor is:

a) Non-zero and constant
b) Zero in electrostatic equilibrium
c) Maximum at the center
d) Dependent on the external electric field
Answer: b) Zero in electrostatic equilibrium

38. The force on a charge in an electric field is given by:

a) F=qEF = qEF=qE
b) F=EqF = \frac{E}{q}F=qE​
c) F=E⋅qϵ0F = \frac{E \cdot q}{\epsilon_0}F=ϵ0​E⋅q​
d) F=qEF = \frac{q}{E}F=Eq​
Answer: a) F=qEF = qEF=qE

39. The electric potential difference between two points is:

a) The work done per unit charge in moving a charge from one point to the other
b) The force per unit charge at one of the points
c) The energy stored in the electric field between the two points
d) The sum of the electric field intensities at the two points
Answer: a) The work done per unit charge in moving a charge from one point to the other

40. The electric field inside a uniformly charged solid sphere is given by:

a) E=Q4πϵ0r2E = \frac{Q}{4\pi \epsilon_0 r^2}E=4πϵ0​r2Q​
b) E=Q4πϵ0R2E = \frac{Q}{4\pi \epsilon_0 R^2}E=4πϵ0​R2Q​
c) E=Q4πϵ0rR3E = \frac{Q}{4\pi \epsilon_0} \frac{r}{R^3}E=4πϵ0​Q​R3r​
d) E=Q4πϵ0r2R3E = \frac{Q}{4\pi \epsilon_0} \frac{r^2}{R^3}E=4πϵ0​Q​R3r2​
Answer: c) E=Q4πϵ0rR3E = \frac{Q}{4\pi \epsilon_0} \frac{r}{R^3}E=4πϵ0​Q​R3r​

41. The electric field outside a charged spherical conductor is:

a) Same as if all the charge were concentrated at the center
b) Zero
c) Directly proportional to the distance from the center
d) Inversely proportional to the distance from the center
Answer: a) Same as if all the charge were concentrated at the center

42. In a parallel plate capacitor, the capacitance is affected by:

a) The area of the plates
b) The separation between the plates
c) The dielectric material between the plates
d) All of the above
Answer: d) All of the above

43. The potential difference between two points is zero if:

a) The points are at the same electric potential
b) The points are at different electric potentials
c) The electric field between the points is maximum
d) The electric field between the points is minimum
Answer: a) The points are at the same electric potential

44. The electric potential due to a uniformly charged ring at a point on its axis is given by:

a) V=kQr2+z2V = \frac{kQ}{\sqrt{r^2 + z^2}}V=r2+z2​kQ​
b) V=kQr2+z2V = \frac{kQ}{r^2 + z^2}V=r2+z2kQ​
c) V=kQr2−z2V = \frac{kQ}{\sqrt{r^2 – z^2}}V=r2−z2​kQ​
d) V=kQr2−z2V = \frac{kQ}{r^2 – z^2}V=r2−z2kQ​
Answer: a) V=kQr2+z2V = \frac{kQ}{\sqrt{r^2 + z^2}}V=r2+z2​kQ​

45. The concept of electric potential is useful because:

a) It helps in calculating the electric field
b) It simplifies the calculation of work done in moving charges
c) It provides a measure of the energy stored in an electric field
d) All of the above
Answer: d) All of the above

46. The force between two point charges in a vacuum is reduced to one-fourth if:

a) The distance between the charges is doubled
b) The distance between the charges is halved
c) The charges are doubled
d) The charges are halved
Answer: a) The distance between the charges is doubled

47. The electric field lines for a positive point charge:

a) Point radially inward
b) Point radially outward
c) Are circular around the charge
d) Are parallel lines
Answer: b) Point radially outward

48. The electric potential inside a uniformly charged spherical shell is:

a) Zero
b) Same as outside the shell
c) Constant and equal to the potential at the surface
d) Varies with the distance from the center
Answer: c) Constant and equal to the potential at the surface

49. The concept of electric field can be best visualized using:

a) Electric field lines
b) Electric potential
c) Capacitance
d) Dielectric constant
Answer: a) Electric field lines

50. The work done in moving a charge in an electric field depends on:

a) The initial and final positions of the charge
b) The path taken by the charge
c) The medium through which the charge is moved
d) The type of charge being moved
Answer: a) The initial and final positions of the charge