Dielectrics and Polarisation - UNSOLVED PRACTICE SET

Q7. Define electric potential at a point. Why is the reference point taken at infinity?

Q8. Distinguish between electric potential and electric potential difference with a simple example.

Q9. A student connects the terminals of a 9V battery to two metal plates. Explain what "9V" means in terms of work done per unit charge.

Q10. Why is electric potential a scalar quantity while electric field is a vector quantity?

Q11. The potential difference between two points A and B in a uniform electric field is 20 V. A charge of +3 μC is moved from A to B. Calculate the work done by the electric field.

Q12. Can electric potential exist at a point where electric field is zero? Give an example to support your answer.

Q13. Derive the expression for the electric potential at a point due to a point charge Q. Explain why the potential is positive for a positive charge and negative for a negative charge.

Q14. Explain the concept of electric potential difference with a real-life analogy (like water flow or height difference). How does potential difference cause charges to move in a conductor?

Q15. In a uniform electric field E = 500 N/C directed along the positive x-axis, points A and B are located at x = 0 and x = 20 cm respectively.

(a) Calculate the potential difference Vₐ − Vᵦ.  

(b) How much work is done by the electric field in moving a charge q = +4 μC from A to B?  

(c) If the charge is moved from B back to A, what is the work done by the external agent?

Q16. A point charge Q = +6 μC is placed at the origin in vacuum.

(a) Calculate the electric potential at a point P located 30 cm from the charge.  

(b) Find the electric potential at a point Q located 60 cm from the charge.  

(c) Calculate the work done by an external agent in moving a test charge q = +2 μC from point Q to point P.  

(d) What is the work done by the electric field in this process?

[Given: k = 9 × 10⁹ N m² C⁻²]

Q17. In your school's physics lab, two large parallel metal plates are connected to a 12V battery. The plates are 4 cm apart and create a uniform electric field between them.

(a) Calculate the electric field between the plates.  

(b) An electron is released from rest at the negative plate. Calculate its speed just before it hits the positive plate.  

(c) How much kinetic energy does the electron gain? Express your answer in electron-volts (eV).  

(d) If the plate separation is doubled while keeping the battery connected, what happens to the electric field and the electron's final speed?

[Given: e = 1.6 × 10⁻¹⁹ C, mₑ = 9.1 × 10⁻³¹ kg]

Q18. Three point charges are placed on the x-axis: q₁ = +2 μC at x = 0, q₂ = −3 μC at x = 20 cm, and q₃ = +4 μC at x = 50 cm.

(a) Calculate the electric potential at x = 30 cm due to all three charges.  

(b) Calculate the electric potential at x = 10 cm.  

(c) Find the work done in moving a charge q = +1 μC from x = 10 cm to x = 30 cm.  

(d) Is this work done by the field or by an external agent? Explain.

[Given: k = 9 × 10⁹ N m² C⁻²]