KVPY2016PhysicsElectrostatics
An electric field due to a positively charged long straight wire at a distance r from it is proportional to r ⁻¹ in magnitude. Two electrons are orbiting such a long straight wire in circular orbits of radii 1 Å and 2 Å . The ratio of their respective time periods is
Options
- A1: 1
- B1: 2
- C2: 1
- D4: 1
Correct answer
B. 1: 2
Step-by-step solution
array l E= K r F = qE array for 1^ s electron. array l (q) 1 r ₁ = mv ₁² r ₁ q = mv ₁² v ₁ ²= q M v ₁= q M array Similarly v ₂= q M array l v ₁= v ₂ T ₁ ~T ₂ = 2 nR ₁ v ₁ 2 n R ₂ v ₂ = 2 nR ₁ v ₁ v ₂ 2 n R ₂ = R ₁ v ₁ v ₂ R ₂ = 1 2 array