MHT CET · Physics · Electrostatics
The charges \(2 \mathrm{q},-\mathrm{q},-\mathrm{q}\) are located at the vertices of an equilateral triangle. At the circumference of the triangle
- A the field is zero but potential is not zero.
- B the field is non-zero but the potential is zero.
- C both, field and potential are zero.
- D both, field and potential are non-zero.
Answer & Solution
Correct Answer
(B) the field is non-zero but the potential is zero.
Step-by-step Solution
Detailed explanation
From charge configuration, at the centre electric field is non-zero.
Potential at the centre due to \(2 \mathrm{q}\) charge \(\mathrm{V}_{2 \mathrm{q}}=\frac{2 \mathrm{q}}{\mathrm{r}}\) and potential due to \(-\mathrm{q}\) charge \(\mathrm{V}_{-\mathrm{q}}=-\frac{\mathrm{q}}{\mathrm{r}} \quad(\mathrm{r}=\) distance of centre point \()\)
\(\therefore \quad\) total potential \(\mathrm{V}=\mathrm{V}_{2 \mathrm{q}}+\mathrm{V}_{-\mathrm{q}}+\mathrm{V}_{-\mathrm{q}}=0\)
Potential at the centre due to \(2 \mathrm{q}\) charge \(\mathrm{V}_{2 \mathrm{q}}=\frac{2 \mathrm{q}}{\mathrm{r}}\) and potential due to \(-\mathrm{q}\) charge \(\mathrm{V}_{-\mathrm{q}}=-\frac{\mathrm{q}}{\mathrm{r}} \quad(\mathrm{r}=\) distance of centre point \()\)
\(\therefore \quad\) total potential \(\mathrm{V}=\mathrm{V}_{2 \mathrm{q}}+\mathrm{V}_{-\mathrm{q}}+\mathrm{V}_{-\mathrm{q}}=0\)
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