Question:medium

A uniform electric field of $5 \times 10^3\text{ N C}^{-1}$ is maintained in the positive Y-direction. Now a point charge of $2 \times 10^{-4}\text{ C}$ at rest is released from the origin. The kinetic energy attained by the charge when it is at a distance of $5\text{ m}$ from the origin is:

Show Hint

Work is simply force times displacement. Group the coefficients together: $(2 \times 5 \times 5) = 50$, then combine the powers of ten: $10^{-4} \times 10^3 = 10^{-1}$. This gives $50 \times 0.1 = 5\text{ J}$ in a single mental calculation step.
Updated On: May 20, 2026
  • $25\text{ J}$
  • $10\text{ J}$
  • $5\text{ J}$
  • $50\text{ J}$
Show Solution

The Correct Option is C

Solution and Explanation

Understanding the Concept: When a charged body moves through a uniform electric field $\vec{E}$, it experiences a constant force $\vec{F} = q\vec{E}$. The work done by this electric field over a displacement vector $\vec{d}$ parallel to the lines of force equals the system's kinetic energy gain: \[ K = W = F \cdot d = q \cdot E \cdot d \]
Step 1: Verify alignment and compute work value components.
We are given:
Electric Field magnitude, $E = 5 \times 10^3\text{ N C}^{-1}$ along $+\hat{j}$
Charge value, $q = 2 \times 10^{-4}\text{ C}$
Distance along movement path, $d = 5\text{ m}$
Since the charge is positive and released from rest, it moves directly along the field lines parallel to the Y-axis. The work done is: \[ W = (2 \times 10^{-4}\text{ C}) \times (5 \times 10^3\text{ N C}^{-1}) \times (5\text{ m}) \]
Step 2: Evaluate numerical multiplication terms.
\[ W = 2 \times 5 \times 5 \times 10^{-4} \times 10^3 = 50 \times 10^{-1} = 5\text{ J} \] Since the particle started from rest ($K_{\text{initial}} = 0$), the kinetic energy attained is equal to the work done, which is $5\text{ J}$.
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