Charged Particle Motion · Field Switching

Watch the particle turn into a descending helix

The canvas is only for the motion: first the electric field shapes the launch in the xy plane, then the magnetic field bends the horizontal motion into circles while gravity pulls the particle downward.

Demonstration controls
Time 0.00 s
Zoom 1.0×
Electric field phase0 ≤ t ≤ 0.2 s
Magnetic field phasecircular XZ motion plus vertical fall
B directionalong +y

Calculation sequence

01 / BEFORE SWITCH

Electric field and gravity

Here q/m = 1 C kg⁻¹, so the electric field gives aₓ = 1 m s⁻². Gravity gives aᵧ = -10 m s⁻².

vₓ = 1 + t,   vᵧ = 2 - 10t,   y = 2t - 5t²
02 / AT t = 0.2 s

The particle is at the vertical top

At the switching instant, vᵧ becomes zero and the horizontal speed entering the magnetic field is 1.2 m s⁻¹.

y = 0.20 m,   v = 1.2 m s⁻¹
03 / AFTER SWITCH

Magnetic field makes the XZ motion circular

The magnetic field is along +y, so it bends the horizontal velocity in the XZ plane. Gravity continues to change only y.

R = mv/(qB) = (10⁻⁶×1.2)/(10⁻⁶×6) = 0.20 m
AAt t = 0.3 s, y = 2(0.3) - 5(0.3)² = 0.15 m = 15 cm.
BAt t = 0.4 s, y = 0, so the vertical distance is not 10 cm.
CThe radius after switching on the magnetic field is 20 cm.
DAt t = 0.35 s, y = 8.75 cm, so the particle is not in the XZ plane.
Correct options
Correct options: (A) and (C)