Question

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

• A. 10
• B. $5\sqrt{2}$
• C. $10\sqrt{2}$
• D. 20

Answer 1

Answer: (C)

Given $v_x=10m{s}^{-1}$.
Since the electric field is directed along the $y$ -axis,
the acceleration of the body along the $y$ -direction is
$a_y=\frac{qE}{m}=\frac{10^{-6}\times 10^3}{10^{-3}}=1m{s}^{-2}$
Therefore, the velocity of the body along the $y$ -axis at time $t=10s$ is
$v_y=a_{y}t=1\times 10=10m{s}^{-1}$
$\therefore$ Resultant velocity
$v=\sqrt{v_x^2+v_y^2}$
$=\sqrt{(10{)}^2+(10{)}^2}$
$=10\sqrt{2}m{s}^{-1}$