Question

Charges are placed on the vertices of a square as shown. Let $\overrightarrow{E}$ be the electric field and $V$ be the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then:

• A. $\overrightarrow{E}$ remains unchanged, $V$ changes
• B. Both $\overrightarrow{E}$ and $V$ change
• C. $\overrightarrow{E}$ and $V$ remain unchanged
• D. $\overrightarrow{E}$ changes, $V$ remains unchanged

Answer 1

Answer: (D)

$\overrightarrow{E}$ changes, $V$ remains unchanged

Let d- distance between any vertex and the center.

The potential at center before and after the charges are interchanged $=\frac{1}{4\pi ϵ}\frac{q}{d}+\frac{1}{4\pi ϵ}\frac{q}{d}+\frac{1}{4\pi ϵ}\frac{-q}{d}+\frac{1}{4\pi ϵ}\frac{-q}{d}$

Field initially at center $=4\frac{1}{4\pi ϵ}\frac{q}{d^2}cos\left(\frac{\pi }{4}\right)$ from A to C

Field at center after interchanging the charges $=4\frac{1}{4\pi ϵ}\frac{q}{d^2}cos\left(\frac{\pi }{4}\right)$ from C to A

The direction of field has changed.