The work done in moving a charge $+Q $ across two points having a potential difference $ K $ is:

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Examoogle · Accepted Answer

The correct answer is Option A: $QK$. The work done in moving a charge across two points in an electric field is equal to the product of the magnitude of the charge and the potential difference between those two points. Mathematically, $W = Q 	imes V$ (or $QK$), where $Q$ is the charge and $K$ is the potential difference.

Step-by-Step Solution & Concepts:
The work done in moving a charge across two points in an electric field is equal to the product of the magnitude of the charge and the potential difference between those two points. Mathematically, $W = Q 	imes V$ (or $QK$), where $Q$ is the charge and $K$ is the potential difference.

Working Principle: Electric potential difference ($V$ or $K$) between two points is defined as the work done ($W$) per unit positive test charge ($Q$) in moving it from one point to the other against electrostatic forces: $$V = \frac{W}{Q}$$ Rearranging this formula for work done gives: $$W = Q 	imes V$$ Substituting $V = K$, we get $$W = QK$.

Key Formulas: $W = Q 	imes V$ — Work done equals charge multiplied by potential difference; $V = \frac{W}{Q}$ — Definition of electric potential difference

Key Points: Work done is independent of the path taken between two points in an electrostatic field (conservative force).; The SI unit of work done is Joule (J) or Electron-volt (eV).; Potential difference $K$ is measured in Volts (V).

Advantages: Fundamental relation for calculating electrostatic energy changes.

Disadvantages: Assumes uniform or defined potential difference between the points.

Applications: Calculating kinetic energy acquired by charged particles in particle accelerators.; Determining energy stored in capacitors and electrical circuits.

Additional Info: Option A ($QK$) is correct because $W = Q 	imes 	ext{Potential Difference}$.. Options B, C, and D introduce incorrect factors such as 2, 1/4, or 1/2 which are dimensionally inconsistent.

Answer: A is correct — The work done in moving a charge +Q across a potential difference K is given by W = QK.

Exam Tip: Always check the units: Charge (Coulombs) × Potential Difference (Volts) = Energy (Joules).

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