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Class 12  »  Physics  »  Electrostatic Potential and Capacitance

Conductors in Electrostatic Fields - UNSOLVED PRACTICE SET

Class 12

Chapter: Electrostatic Potential and Capacitance | Topic: Conductors in Electrostatic Fields

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Class 12

CONDUCTORS IN ELECTROSTATIC FIELDS - UNSOLVED PRACTICE SET

Topic: Conductors in Electrostatic Fields

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

Multiple Choice Questions

Q1. Inside a conductor in electrostatic equilibrium, the electric field is:

  1. Maximum
  2. Zero
  3. Constant
  4. Equal to the field at the surface

Q2. The electric potential inside a charged conductor in electrostatic equilibrium:

  1. Varies with distance from the center
  2. Is constant throughout the conductor
  3. Is maximum at the center
  4. Is zero everywhere

Q3. Excess charge on a conductor in electrostatic equilibrium resides:

  1. Uniformly throughout the volume
  2. Only on the outer surface
  3. Only at the center
  4. Both inside and on the surface

Q4. The electric field just outside a charged conducting surface is:

  1. Parallel to the surface
  2. Perpendicular to the surface
  3. At 45° to the surface
  4. Zero

Q5. For a charged conductor, the surface charge density is:

  1. Uniform everywhere on the surface
  2. Maximum at flat portions
  3. Maximum at sharp points or corners
  4. Zero everywhere

Q6. When a conductor is placed in an external electric field, the charges redistribute themselves by the process of:

  1. Conduction
  2. Induction
  3. Radiation
  4. Polarization

Short Answer Questions

Q7. Why is the electric field inside a conductor zero in electrostatic equilibrium? Explain using the concept of free electrons.

Q8. Explain why the surface of a charged conductor is an equipotential surface.

Q9. A hollow charged conductor has a small hole. Does any electric field exist inside the cavity? Explain.

Q10. Why does a charged conductor lose its charge when connected to the Earth? Explain the process of grounding.

Q11. Why are lightning rods made with sharp pointed tips? Explain in terms of surface charge density and electric field.

Q12. A neutral conducting sphere is placed in a uniform external electric field. Describe the charge distribution on the sphere.

Long Answer Questions

Q13. State and explain the properties of a conductor in electrostatic equilibrium. Why is the electric field inside a conductor zero? Why does charge reside only on the outer surface?

Q14. Explain electrostatic shielding (Faraday cage effect). How does a conducting enclosure protect its interior from external electric fields? Give two real-life applications.

Q15. A solid conducting sphere of radius 10 cm carries a charge of +20 μC. It is surrounded by a concentric conducting spherical shell of inner radius 15 cm and outer radius 20 cm, carrying a charge of −10 μC.

(a) Find the charge distribution on the inner and outer surfaces of the shell.

(b) Calculate the electric field at r = 5 cm, r = 12 cm, and r = 25 cm.

(c) What is the potential of the inner sphere?

[Given: k = 9 × 10⁹ N m² C⁻²]

Numerical / Application-Based Problems

Q16. A solid conducting sphere of radius 5 cm carries a total charge Q = +8 μC.

(a) Calculate the surface charge density on the sphere.

(b) Find the electric field just outside the surface of the sphere.

(c) Calculate the electric potential at the surface of the sphere.

(d) If the sphere is connected to a distant second conducting sphere of radius 10 cm (initially uncharged) by a long thin wire, what is the final charge on each sphere?

[Given: k = 9 × 10⁹ N m² C⁻²]

Q17. In your school physics lab, you have a hollow metal can with a small opening at the top. You charge a small metal ball and lower it into the can using an insulating thread.

(a) Describe what happens to the charge distribution on the inner and outer surfaces of the can as the ball is lowered inside.

(b) When the ball touches the inner surface of the can, what happens to the charge on the ball? Explain using the properties of conductors.

(c) If the can is now connected to the ground, what happens to its charge?

(d) This experiment is called the "ice pail experiment." Explain its significance in demonstrating a property of conductors.

Q18. Two concentric hollow conducting spheres have radii R₁ = 8 cm and R₂ = 12 cm. The inner sphere carries charge +q = +6 μC and the outer sphere carries charge +Q = +10 μC.

(a) Find the charge distribution on all surfaces.

(b) Calculate the electric field in the regions: r < R₁, R₁ < r < R₂, and r > R₂.

(c) Find the potential difference between the two spheres.

(d) If the outer sphere is grounded (connected to Earth), what is the new charge on its outer surface? What is the new potential difference?

[Given: k = 9 × 10⁹ N m² C⁻²]


Total: 30 Marks | Time: 40 mins

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