Potential Energy of a System of Charges - UNSOLVED PRACTICE SET
Chapter: Electrostatic Potential and Capacitance | Topic: Potential Energy of a System of Charges
POTENTIAL ENERGY OF A SYSTEM OF CHARGES - UNSOLVED PRACTICE SET
Topic: Potential Energy of a System of Charges
Multiple Choice Questions
Q1. The potential energy of a system of two point charges q₁ and q₂ separated by distance r is:
- kq₁q₂/r²
- kq₁q₂/r
- kq₁q₂r
- k(q₁ + q₂)/r
Q2. The potential energy of a system of charges is:
- Always positive
- Always negative
- Can be positive or negative
- Always zero
Q3. For a system of three charges, the total potential energy is:
- The sum of potential energies of all possible pairs
- The product of individual potential energies
- The average of individual potential energies
- Equal to the potential energy of any one pair
Q4. Work done in assembling a system of charges from infinity is stored as:
- Kinetic energy
- Potential energy
- Thermal energy
- Light energy
Q5. For two like charges, the potential energy of the system is:
- Positive
- Negative
- Zero
- Infinite
Q6. The potential energy of an electric dipole placed in a uniform electric field E making angle θ with the field is:
- pE sin θ
- −pE cos θ
- pE cos θ
- −pE sin θ
Short Answer Questions
Q7. Define the potential energy of a system of two point charges. When is it positive and when is it negative?
Q8. Two charges +q and +q are brought from infinity to a distance d apart. Is the work done by the external agent positive or negative? Explain.
Q9. Write the expression for the potential energy of a system of three charges q₁, q₂, and q₃ placed at the vertices of a triangle.
Q10. Why is the potential energy of a system of two opposite charges negative? What does the negative sign signify?
Q11. An electric dipole with dipole moment p is placed parallel to a uniform electric field E. What is its potential energy? What happens if it is rotated to become anti-parallel?
Q12. Two electrons are placed 1 Å apart. Calculate the potential energy of this system.
[Given: k = 9 × 10⁹ N m² C⁻², e = 1.6 × 10⁻¹⁹ C]
Long Answer Questions
Q13. Derive the expression for the potential energy of a system of two point charges. Explain the physical significance of the sign of the potential energy.
Q14. Derive the expression for the potential energy of an electric dipole placed in a uniform electric field. Show that the potential energy is minimum when the dipole is aligned with the field and maximum when it is anti-aligned.
Q15. Three charges are placed at the corners of an equilateral triangle of side 10 cm: q₁ = +2 μC, q₂ = +2 μC, and q₃ = −2 μC.
(a) Calculate the potential energy of the system.
(b) Calculate the work done in bringing these charges from infinity to their present positions.
(c) If charge q₃ is removed to infinity, what is the change in potential energy of the remaining system?
[Given: k = 9 × 10⁹ N m² C⁻²]
Numerical / Application-Based Problems
Q16. Four identical charges q = +1 μC are placed at the four corners of a square of side 20 cm.
(a) Calculate the potential energy of the system.
(b) Calculate the work required to assemble this system from infinity.
(c) If one charge is removed from a corner, what is the new potential energy of the remaining three charges?
(d) How much work is done by the electric field when the fourth charge is removed to infinity?
[Given: k = 9 × 10⁹ N m² C⁻²]
Q17. In a simplified model of a hydrogen atom, an electron orbits a proton at a distance of 0.53 Å (Bohr radius).
(a) Calculate the potential energy of the electron-proton system.
(b) Calculate the total energy of the electron (kinetic + potential).
(c) The ionization energy is the energy required to remove the electron to infinity. Calculate the ionization energy in eV.
(d) Explain why the total energy is negative and what this means physically.
[Given: k = 9 × 10⁹ N m² C⁻², e = 1.6 × 10⁻¹⁹ C, mₑ = 9.1 × 10⁻³¹ kg]
Q18. An electric dipole with dipole moment p = 2 × 10⁻⁸ C m is placed in a uniform electric field E = 5 × 10⁴ N/C.
(a) Calculate the potential energy when the dipole is (i) parallel, (ii) perpendicular, and (iii) anti-parallel to the field.
(b) Calculate the work done by an external agent in rotating the dipole from parallel to anti-parallel orientation.
(c) At what angle is the potential energy half of its minimum value?
(d) Sketch a graph of potential energy versus angle θ for 0° ≤ θ ≤ 360°.