Question

If four charges \(+12\,\text{nC}, -20\,\text{nC}, +32\,\text{nC}\) and \(-15\,\text{nC}\) are arranged at the four vertices of a square of side \(\sqrt{2}\,\text{m}\), then the net electric potential at the centre of the square due to these four charges is

• A. \(72\,\text{V}\)
• B. \(81\,\text{V}\)
• C. \(64\,\text{V}\)
• D. \(36\,\text{V}\)

Hint:

Electric potential is a scalar quantity, so it can be added algebraically even if the charges are at different locations.

Answer 1

The Correct Option is B

Step 1: The distance of the centre of the square from each vertex is: \[ r = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}\,\text{m} \] Step 2: Use the formula for electric potential at a point: \[ V = \frac{1}{4\pi \varepsilon_0} \sum \frac{q_i}{r} \] Step 3: Total charge: \[ q_{\text{net}} = (+12 - 20 + 32 - 15)\,\text{nC} = 9\,\text{nC} = 9 \times 10^{-9}\,\text{C} \] Step 4: Electric potential: \[ V = \frac{1}{4\pi \varepsilon_0} . \frac{9 \times 10^{-9}}{1/\sqrt{2}} = 9 \times 10^9 . 9 \times 10^{-9} . \sqrt{2} = 81 \sqrt{2} \approx 81\,\text{V} \]