MHTCET 20 Apr 2026 Shift 1 Paper

Concept:Electric potential is a scalar quantity, so the net potential at a point is the algebraic sum of potentials due to all charges.Explanation:The four charges are placed in order around the square, so the two negative charges occupy adjacent corners.The midpoint lies on the side joining these two negative charges.Since the side of the square is $2r$, the distance from this midpoint to each negative charge is $r$.For each positive charge, the horizontal distance to the midpoint is $r$, and the vertical distance is $2r$.Using Pythagoras' theorem, the distance from each positive charge to the midpoint is:$$\sqrt{r^2 + (2r)^2} = r\sqrt{5}$$Now add potentials due to all four charges algebraically:$$V = \frac{1}{4\pi\epsilon_0}\left[\frac{q}{r\sqrt{5}} + \frac{q}{r\sqrt{5}} - \frac{q}{r} - \frac{q}{r}\right]$$Simplifying gives:$$V = \frac{1}{4\pi\epsilon_0} \frac{2q}{r}\left(\frac{1}{\sqrt{5}} - 1\right)$$Answer:The correct option is A: $\frac{1}{4 \pi \epsilon_{0}} \frac{2 q}{r}\left[\frac{1}{\sqrt{5}}-1\right]$