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Superposition and Continuous Charges
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Superposition and Continuous Charges JEE Main Physics Fill Blank-1
⚡ Part 1: Superposition Principle (Fill in the Blanks)
1. The electric field due to a system of charges is the ________ sum of electric fields due to individual charges.
2. If two point charges +3μC and -5μC are placed 4 cm apart, the net force on a third charge +2μC placed at the midpoint is ________ N. (Use k = 9×10⁹ N·m²/C²)
3. Four equal charges of magnitude q are placed at the corners of a square of side 'a'. The electric field at the centre of the square is ________.
4. The principle of superposition is valid because electric field follows ________ law and electrostatic force is a ________ force.
5. When applying superposition principle, we add electric fields ________ but add electric potentials ________.
6. Two charges +q and -q are separated by distance 2a. The electric field at a point on the perpendicular bisector at distance 'r' from the midpoint (where r >> a) varies as ________.
7. The electric field due to n point charges is given by E⃗ = ________ where r⃗ᵢ is the position vector of the field point from the ith charge.
🔄 Part 2: Continuous Charge Distributions (Fill in the Blanks)
8. For a continuous charge distribution, the electric field is given by dE⃗ = ________ where dq is an infinitesimal charge element.
9. The linear charge density λ has units of ________ and is defined as ________.
10. For a uniformly charged ring of radius R and total charge Q, the electric field at the centre is ________.
11. The electric field at a distance 'x' along the axis of a uniformly charged ring of radius R and charge Q is E = ________.
12. For a uniformly charged infinite line with linear charge density λ, the electric field at perpendicular distance 'r' is E = ________.
13. The electric field due to an infinite plane sheet of surface charge density σ is E = ________ and is ________ to the sheet.
14. For a uniformly charged disc of radius R and surface charge density σ, the electric field at the centre is ________.
🎯 Part 3: Advanced Applications (Fill in the Blanks)
15. The electric field at a distance 'x' along the axis of a uniformly charged disc of radius R approaches ________ when x >> R.
16. For a semicircular ring of radius R with uniform linear charge density λ, the electric field at the centre has magnitude ________ and direction ________.
17. The electric field inside a uniformly charged spherical shell of radius R is ________ everywhere.
18. For two parallel infinite sheets with surface charge densities +σ and -σ separated by distance d, the electric field between the sheets is ________ and outside the sheets is ________.
19. The electric field at a distance 'r' from the centre of a uniformly charged solid sphere of radius R and total charge Q (where r < R) is E = ________.
20. When a point charge q is placed at distance 'h' above an infinite grounded conducting plane, the force on the charge is ________ where the image charge is located at ________.
📋 Answer Key
Answers:
1. vector
2. 6.75×10⁻³
3. zero
4. linear, conservative
5. vectorially, algebraically
6. 1/r³
7. (1/4πε₀) Σᵢ (qᵢ/rᵢ²) r̂ᵢ
8. (1/4πε₀) (dq/r²) r̂
9. C/m, charge per unit length
10. zero
11. (1/4πε₀) × (Qx)/(x²+R²)³/²
12. λ/(2πε₀r)
13. σ/(2ε₀), perpendicular
14. zero
15. σ/(2ε₀)
16. λ/(2π²ε₀R), along perpendicular bisector
17. zero
18. σ/ε₀, zero
19. (1/4πε₀) × (Qr)/R³
20. q²/(16πε₀h²), distance h below the plane
1. vector
2. 6.75×10⁻³
3. zero
4. linear, conservative
5. vectorially, algebraically
6. 1/r³
7. (1/4πε₀) Σᵢ (qᵢ/rᵢ²) r̂ᵢ
8. (1/4πε₀) (dq/r²) r̂
9. C/m, charge per unit length
10. zero
11. (1/4πε₀) × (Qx)/(x²+R²)³/²
12. λ/(2πε₀r)
13. σ/(2ε₀), perpendicular
14. zero
15. σ/(2ε₀)
16. λ/(2π²ε₀R), along perpendicular bisector
17. zero
18. σ/ε₀, zero
19. (1/4πε₀) × (Qr)/R³
20. q²/(16πε₀h²), distance h below the plane
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