Question

A particle of mass m carrying charge +q1 is revolving around a fixed charge -q2 in a circular orbit of radius r.what is the period of revilution

Answer 1

When a particle of mass m carrying charge +q₁ is revolving around a fixed charge -q₂ in circular orbit of radius r then, centrifugal force balances the electrostatic force acted between q₁ and q₂.
e.g., centrifugal force = electrostatic force
mω²r = kq₁q₂/r² , here ω is angular frequency so, ω = 2π/T , T is time period
m{2π/T}² = kq₁q₂/r³
m× 4π²/T² = kq₁q₂/r³
T² = mr³4π²/kq₁q₂
Take square root both sides,
T = 2π√{mr³/kq₁q₂}

Hence, time period is T = 2π√{mr³/kq₁q₂}