In a vacuum chamber, a particle of charge 1 μC and mass 1 mg is projected with a velocity (î + 2ĵ) m s⁻¹ from the XZ plane at time t = 0 in an electric field of 1î V m⁻¹. At t = 0.2 s, the electric field is switched off and a magnetic field of 6ĵ T is switched on. The acceleration due to gravity is -10ĵ m s⁻². Correct option(s) is/are:
Select all that apply

Question

In a vacuum chamber, a particle of charge 1 μC and mass 1 mg is projected with a velocity (î + 2ĵ) m s⁻¹ from the XZ plane at time t = 0 in an electric field of 1î V m⁻¹. At t = 0.2 s, the electric field is switched off and a magnetic field of 6ĵ T is switched on. The acceleration due to gravity is -10ĵ m s⁻². Correct option(s) is/are:

Select all that apply

G1 Physics · Accepted Answer

For 0 ≤ t ≤ 0.2 s, vertical motion has uᵧ = 2 m s⁻¹ and aᵧ = −10 m s⁻², so at t = 0.2 s the vertical speed becomes zero and y = 2(0.2) − 5(0.2)² = 0.20 m. The electric field accelerates the particle along +x by qE/m = 1 m s⁻², so vₓ at 0.2 s is 1.2 m s⁻¹. In B = 6ĵ T, the x-z motion is circular with radius r = mv⊥/(qB) = (10⁻⁶×1.2)/(10⁻⁶×6) = 0.20 m. Gravity subsequently gives y = 0.20 − 5(t−0.2)², hence at t = 0.3 s, y = 0.15 m. Thus A and C are correct.