Question

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

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

Answer 1

Answer: (C)

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