Question

An electric charge enters in electric field at right angles to the direction of electric field. What is the nature of the path followed?

Answer 1

Let the electric field be E with potential V and electron entering at 90° and distance traveled d, and 2points are d distance apart

Therefore force on electron,

$F=eE=\frac{eV}{d}$ (i) and

$F=ma$ (ii)

From 1 and 2

$\frac{eV}{d}=ma$ (a)

a orce is applied thus electron must accelerate in its direction and

$a=2\frac{y}{t^2}$ (iii)

[Using $y=ut+\frac{1}{2}a{t}^2$

Therefore equation (a) becomes

$\frac{eV}{d}=ma=\frac{2my}{t^2}=\frac{2my{V}^2}{x^2}$ (iv)

Using $t=\frac{V}{x}$

From equation (iv)

$y-\left[\frac{eV}{2dm{V}^2}\right]x^2$

Thus the path followed by electron must be parabolic.