First slide

Motion of charged particle in uniform electric field

Question

There is a uniform electric field of strength $10^{3}$ V /m along y-axis. A body of mass 1 gm and charge $10^{- 6}$ C is projected into the field from origin along the positive x-axis with a velocity 10 m/s. Its speed in m/s after 10 s is (Neglect gravitation)

Moderate

A

10
B

$5 \sqrt{2}$
C

$10 \sqrt{2}$
D

20

Solution

Body moves along the parabolic path.
For vertical motion: By using v = u + at, we have
$v_{y} = 0 + \frac{QE}{m} . t = \frac{10^{- 6} \times 10^{3}}{10^{- 3}} \times 10 = 10 m / s$
For horizontal motion: Its horizontal velocity remains the same, i.e., after 10 s, horizontal velocity of body $v_{x}$ = 10 m/s.
Velocity after 10 s, v = $\sqrt{v_{x}^{2} + v_{y}^{2}}$ = 10✓2 m/s

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