COMEDK · Physics · 17. Electrostatics

Point charge \(\sqrt{2}C, \sqrt{2}C\), and \(-2C\) are placed at the three vertices of a right-angled triangle in air. [as shown in the figure below] What is the electric field at a point P on the hypotenuse that is equidistant from all three charges. Given distances \(XP = YP = ZP = 0.5\ m\)

A \(7\cdot 2 \times 10^9\ NC^{-1}\) along PY
B \(7\cdot 2 \times 10^{10}\ NC^{-1}\) along PY
C \(0\cdot 72 \times 10^9\ NC^{-1}\) along YP
D \(0\cdot 72 \times 10^{10}\ NC^{-1}\) along YP

Verified Solution

Answer & Solution

Correct Answer

(B) \(7\cdot 2 \times 10^{10}\ NC^{-1}\) along PY

Step-by-step Solution

Detailed explanation

Let the charges at vertices \(X\), \(Y\), and \(Z\) be \(q_X = \sqrt{2}\ C\), \(q_Y = -2\ C\), and \(q_Z = \sqrt{2}\ C\) respectively. Point \(P\) is on the hypotenuse \(XZ\) and is equidistant from \(X\) and \(Z\), meaning it is the midpoint of \(XZ\). The electric field at…

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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