Govt. Exams
Entrance Exams
Initial force: F₁ = k(Q)(3Q)/r² = 3kQ²/r². When spheres touch, total charge = 4Q, distributed as 2Q each. Final force: F₂ = k(2Q)(2Q)/r² = 4kQ²/r². Ratio: F₂/F₁ = (4kQ²/r²)/(3kQ²/r²) = 4/3. The force increases by factor 4/3, or changes by 4/3 times initial. However, comparing initial to final: change factor = F₂/F₁ = 4/3. The force becomes (4/3) times, meaning it changed by multiplying with 4/3. If asking reduction: Answer is 2/3 represents the comparative analysis in different context, but correct ratio of final to initial is 4/3.
For an infinite line charge, E = λ/(2πε₀r). Substituting: E = (2 × 10⁻⁸)/(2π × 8.85 × 10⁻¹² × 0.1) = (2 × 10⁻⁸)/(5.57 × 10⁻¹²) ≈ 3.6 × 10³ N/C
Introducing a dielectric increases capacitance by factor κ: C = κε₀A/d = κC₀. This is a fundamental property used in capacitor design.
The electric field is related to potential by E = -dV/dr (negative gradient of potential). The negative sign indicates field points toward lower potential.
Motional EMF in a rod moving perpendicular to magnetic field: ε = BvL. This creates charge separation until electric field balances magnetic force.
At point (x, 0): V = kq/x - kq/(a-x) = 0 gives x = a-x, so x = a/2. The midpoint has zero potential.
Using Gauss's law for an infinite plane: E = σ/(2ε₀). The field is independent of distance and perpendicular to the plane.
By Gauss's law, for a uniformly charged spherical shell, the electric field inside (r < R) is zero because the enclosed charge is zero.
When identical conducting spheres touch, charge distributes equally. Total charge = +Q + (-Q) = 0, so each gets 0. They remain neutral after separation.
Work done by electric field = Change in kinetic energy. W = qEd = eEd, which equals kinetic energy since initial KE = 0.
