Superposition Principle - UNSOLVED PRACTICE SET
Chapter: Electric Charges and Fields | Topic: Superposition Principle
SUPERPOSITION PRINCIPLE - UNSOLVED PRACTICE SET
Topic: Superposition Principle
Multiple Choice Questions
Q1. According to the Superposition Principle, the net force on a charge due to multiple charges is:
- The scalar sum of individual forces
- The vector sum of individual forces
- The product of individual forces
- The average of individual forces
Q2. Three charges are placed at the corners of a triangle. The net force on any one charge is calculated by:
- Adding the magnitudes of forces due to the other two charges
- Adding the forces vectorially using the parallelogram law
- Multiplying the individual forces
- Finding the difference between the two forces
Q3. The Superposition Principle is valid for electrostatic forces because:
- Electrostatic forces are conservative
- Electrostatic forces obey Newton's third law
- The force between two charges is independent of the presence of other charges
- Electrostatic forces are always attractive
Q4. Two charges +q and +q are placed on the x-axis at x = −a and x = +a respectively. A third charge +q is placed at the origin. The net force on the charge at the origin is:
- Zero
- Towards +x direction
- Towards −x direction
- Along the y-axis
Q5. Four equal charges q are placed at the four corners of a square. A fifth charge Q is placed at the center. The net force on Q due to the four corner charges is:
- Zero
- Along one diagonal
- Along both diagonals
- Cannot be determined without knowing the values
Q6. The Superposition Principle does NOT apply to:
- Electrostatic forces
- Gravitational forces
- Nuclear forces at very short distances
- Electric fields
Short Answer Questions
Q7. State the Superposition Principle for electrostatic forces. Why is it called a "vector" superposition?
Q8. Two charges q₁ and q₂ exert forces F₁ and F₂ respectively on a third charge q₃. How do you find the net force on q₃? Write the expression.
Q9. Three charges are placed along a straight line. Explain how you would calculate the net force on the middle charge using the Superposition Principle.
Q10. Why is the Superposition Principle important in electrostatics? Give one practical situation where it is used.
Q11. Two positive charges are placed on the x-axis at x = 0 and x = d. A negative charge is placed at x = d/2. In which direction is the net force on the negative charge?
Q12. Can the Superposition Principle be used to find the net electric field at a point due to multiple charges? Explain briefly.
Long Answer Questions
Q13. Explain the Superposition Principle with a clear example involving three point charges. Show how the net force on one charge is calculated by considering the individual forces from the other two charges separately.
Q14. Four charges +q, +q, −q, and −q are placed at the four corners of a square of side 'a'. Find the net force on the charge +q at one corner due to the other three charges. Draw a diagram showing all the forces.
Q15. Three point charges q₁ = +1 μC, q₂ = +2 μC, and q₃ = −3 μC are placed at the vertices of an equilateral triangle of side 10 cm. Calculate the net force on q₁ due to q₂ and q₃. Show the direction of the net force in a diagram.
[Given: k = 9 × 10⁹ N m² C⁻²]
Numerical / Application-Based Problems
Q16. In a school physics project, three students place charges at the corners of a right-angled triangle ABC, where AB = 3 cm, BC = 4 cm, and ∠B = 90°. The charges are: qₐ = +2 μC at A, qᵦ = −3 μC at B, and qᶜ = +4 μC at C.
(a) Calculate the force on qₐ due to qᵦ.
(b) Calculate the force on qₐ due to qᶜ.
(c) Find the magnitude and direction of the net force on qₐ.
[Given: k = 9 × 10⁹ N m² C⁻²]
Q17. Four identical charges q = +1 μC are placed at the four corners of a square of side 20 cm. A charge Q = −2 μC is placed at the center of the square.
(a) Calculate the force on Q due to one corner charge.
(b) Show that the net force on Q is zero using the Superposition Principle.
(c) If one of the corner charges is removed, what is the magnitude and direction of the net force on Q?
[Given: k = 9 × 10⁹ N m² C⁻²]
Q18. Three charges are placed along the x-axis: q₁ = +4 μC at x = 0, q₂ = −2 μC at x = 30 cm, and q₃ = +3 μC at x = 60 cm.
(a) Calculate the net force on q₂ due to q₁ and q₃.
(b) At what point on the x-axis (other than infinity) should a charge q₄ be placed so that the net force on q₂ is zero?
(c) If q₂ is replaced by a charge of +2 μC, what is the new net force on it?
[Given: k = 9 × 10⁹ N m² C⁻²]