A charged particle (mass m and charge q) moves along the X-axis with velocity v₀. When it passes through the origin it enters a region having a uniform electric field ⃗E=-Êj which extends up to x=d. The equation of the path of the particle in the region xd is

Question

A charged particle (mass m and charge q) moves along the X-axis with velocity v₀. When it passes through the origin it enters a region having a uniform electric field ⃗E=-Êj which extends up to x=d. The equation of the path of the particle in the region x>d is

Accepted Answer

(2) y=(qEd)/(mv₀²)(d/2-x). Inside the field the x-motion is uniform, x=v₀t, while a_y=(qE_y)/m=-(qE)/m. At x=d, i.e. t=d/(v₀): y_d=-1/2(qE)/m(d²)/(v₀²)=-(qEd²)/(2mv₀²) and v_y=-(qEd)/(mv₀). Beyond x=d there is no field, so the particle travels in a straight line of slope (v_y)/(v₀)=-(qEd)/(mv₀²). y=y_d-(qEd)/(mv₀²)(x-d)=-(qEd²)/(2mv₀²)-(qEd)/(mv₀²)x+(qEd²)/(mv₀²). Collecting terms, y=(qEd)/(mv₀²)(d/2-x).

A charged particle (mass m and charge q) moves along the X-axis with velocity v₀. When it passes through the origin it enters a region having a uniform electric field ⃗E=-Êj which extends up to x=d. The equation of the path of the particle in the region x>d is

Step-by-step solution

Why the other options are wrong