08/12/2025
Here are 3 physics questions with long answers:
*1. What is the force between two small charged spheres of charges 2×10^-7 C and 3×10^-7 C placed 30cm apart in air?*
The electrostatic force between the two spheres is given by Coulomb's law as,
F = (1 / 4πε₀) * (q₁q₂ / r²)
where,
q₁ = 2 × 10^-7 C
q₂ = 3 × 10^-7 C
r = 30 cm = 0.3 m
ε₀ = permittivity of free space = 8.85 × 10^-12 F/m
F = (9 × 10^9 N m² C^-2) * (2 × 10^-7 C * 3 × 10^-7 C) / (0.3 m)²
= 6 × 10^-3 N
Since the charges are of the same nature, the force is repulsive. ¹
*2. Obtain the resonant frequency ωr of a series LCR circuit with L = 2.0 H, C = 32 μF, and R = 10 Ω. What is the Q-value of this circuit?*
The resonant frequency ωr is given by,
ωr = 1 / √(LC)
= 1 / √(2 H * 32 × 10^-6 F)
= 125 rad/s
The Q-value is given by,
Q = ωr L / R
= (125 rad/s * 2 H) / 10 Ω
= 25
*3. A long solenoid with 15 turns per cm has a small loop of area 2.0 cm² placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2 A to 4 A in 0.1 s, what is the induced emf in the loop while the current is changing?*
The induced emf ε is given by,
ε = -N(dΦ/dt)
where Φ is the magnetic flux through the loop.
For a solenoid, B = μ₀ n I
Φ = BA = μ₀ n I A
ε = -μ₀ n A (dI/dt)
= -4π × 10^-7 T m A^-1 * 1500 turns/m * 2 × 10^-4 m² * (2 A / 0.1 s)
= 7.54 × 10^-6 V
