Electric Field due to Various Charge Distributions - UNSOLVED PRACTICE SET

Q7. Write the expression for the electric field due to an infinite line charge with linear charge density λ at a perpendicular distance r from it.

Q8. Why is the electric field at the center of a uniformly charged ring zero? Explain with symmetry arguments.

Q9. Compare the electric field due to a point charge and an infinite plane sheet. How do they differ in terms of distance dependence

Q10. A uniformly charged spherical shell has charge Q and radius R. What is the electric field
(a) inside the shell, and
(b) outside the shell at a distance r from the center?

Q11. Two large parallel metal plates carry surface charge densities +σ and −σ. What is the electric field
(a) between the plates, and
(b) outside the plates?

Q12. A charged ring of radius 10 cm has a total charge of +5 μC. What is the direction of the electric field at a point on the axis of the ring, 20 cm from the center?

Q13. Derive an expression for the electric field intensity at a point on the axis of a uniformly charged ring of radius R and total charge Q. Show that at large distances, it behaves like the field of a point charge.

Q14. Derive the expression for the electric field due to an infinite plane sheet of charge with uniform surface charge density σ. Explain why the field is independent of the distance from the sheet.

Q15. A thin spherical shell of radius 15 cm carries a uniform surface charge density σ = 4 × 10⁻⁶ C/m².

(a) Calculate the total charge on the shell.

(b) Find the electric field at a point 10 cm from the center (inside the shell).

(c) Find the electric field at a point 25 cm from the center (outside the shell).

[Given: ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²]

Q16. A uniformly charged ring of radius 20 cm has a total charge Q = +10 μC.

(a) Calculate the electric field at a point on the axis of the ring, 15 cm from the center.

(b) At what distance from the center on the axis is the electric field maximum? Calculate this maximum field.

(c) Verify that at a very large distance (say, 5 m), the field approximately equals that of a point charge.

[Given: k = 9 × 10⁹ N m² C⁻²]

Q17. Two large parallel copper plates are placed 2 cm apart in air. The plates have surface charge densities +σ and −σ, where σ = 5 × 10⁻⁶ C/m².

(a) Calculate the electric field in the region between the plates.

(b) Calculate the electric field in the region outside the plates.

(c) A tiny oil drop of mass 3 × 10⁻¹⁵ kg and charge −2e is placed between the plates. Find the acceleration of the drop. Will it move towards the positive or negative plate?

[Given: ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻², e = 1.6 × 10⁻¹⁹ C]

Q18. An infinite line charge has a linear charge density λ = 3 × 10⁻⁶ C/m. A point charge q = +2 μC is placed at a perpendicular distance of 30 cm from the line.

(a) Calculate the electric field due to the line charge at the position of the point charge.

(b) Find the force experienced by the point charge.

(c) If the point charge is moved to a distance of 60 cm, by what factor does the force change? Explain why this happens.

[Given: k = 9 × 10⁹ N m² C⁻²]