MHT CET · Physics · Electrostatics

Charges of \(2 \mu \mathrm{C}\) and \(-3 \mu \mathrm{C}\) are placed at two points A and B separated by 1 m . The distance of the point from A , where net potential is zero, is

A 0.7 m
B 0.5 m
C 0.4 m
D 0.6 m

Verified Solution

Answer & Solution

Correct Answer

(C) 0.4 m

Step-by-step Solution

Detailed explanation

\(V=\frac{K q}{r}\)
Let \(r_1\) and \(r_2\) be the distances from points \(A\) and B respectively where the potential is zero.
\(\begin{array}{ll}
\therefore \quad & \frac{\mathrm{K}\left(2 \times 10^{-6}\right)}{\mathrm{r}_1}=\frac{\mathrm{K}\left(3 \times 10^{-6}\right)}{\mathrm{r}_2} \\
\therefore \quad & \frac{\mathrm{r}_2}{\mathrm{r}_1}=\frac{3}{2} \\
\therefore \quad & \frac{\mathrm{r}_2+\mathrm{r}_1}{\mathrm{r}_1}=\frac{2+3}{2} \\
\therefore \quad & \frac{1}{r_1}=\frac{5}{2} \ldots\left(\text { given, } r_1+r_2=1 \mathrm{~m}\right) \\
\therefore \quad & r_1=0.4 \mathrm{~m}
\end{array}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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