Electromagnetism - Particle Trajectory

The figure above shows the trajectory of a particle that is deflected as it moves through the uniform electric field between parallel plates. There is potential difference V and distance d between the plates, and they have length L. The particle (mass m, charge q) has non relativistic speed v before it enters the field, and its direction at this time is perpendicular to the field. For small deflections, which of the following expressions is the best approximation to the deflection angle θ?

A. Arctan ( (L/d)(Vq/mv²) )
B. Arctan ( (L/d)(Vq/mv²)² )
C. Arctan ( (L/d)² (Vq/mv²) )
D. Arctan ( (L/d)(2Vq/mv²)^½ )
E. Arctan ( (L/d)^½(2Vq/mv²) )

(GR9677 #71)

Solution:

tan θ = v_y / v_x = at / v 
v  = L/t → t = L/v
F  =  ma = qE = qV / d → a = qV / md

tan θ = at / v =  (qV / md) (L/v) / v = (qVL /mdv²)
→  θ = arctan (qVL /mdv²) = arctan ( (L/d)(Vq/mv²) )

Answer: A

Electromagnetism - Electric and Magnetic Force

A positively charged particle is moving in the xy-plane in a region where there is a non-zero uniform electric magnetic field B in the +z –direction and a non-zero uniform electric field in the +y-direction. Which of the following is a posible trajectory for the particle?

(GR9677 #86)

Solution:

v is in the xy-plane
E is in +y-direction


→ F is in +y-direction
→ particle will be deflected by E in +y-direction

B is in +z-direction


→ F,v, B orthogonal to each other
→ E and B orthogonal to each other

Particle moving in an orthogonal direction with B will exhibit cyclotron (helix shaped motion).                    
Answer:  B