JEE Mains · Physics · STD 12 - 2. Electric potential and capacitance

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at \(P\), in the region, is found to vary between in the limits \(589.0\,V\) to \(589.8\, V\). What is the potential at a point on the sphere whose radius vector makes an angle of \(60^o\) with the direction of the field ?........\(V\)

A \(589.5\)
B \(589.2\)
C \(589.4\)
D \(589.6\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(589.4\)

Step-by-step Solution

Detailed explanation

Potential gradient is given by, \(\Delta \mathrm{V}=\mathrm{E} . \mathrm{d}\) \(0.8=\mathrm{Ed}(\mathrm{max})\) \(\Delta V=E d \cos \theta=0.8 \times \cos 60=0.4\) Hence, maximum potential at a point on the sphere \(=589.4\, \mathrm{V}\)

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.

Same subject

Match List \(I\) with List \(II\)

List \(I\)	List \(II\)
\((A)\) Young's Modulus \((Y)\)	\((I)\) \(\left[ M L ^{-1} T ^{-1}\right]\)
\((B)\) Co-efficient of Viscosity \((\eta)\)	\((II)\) \(\left[ M L ^2 T ^{-1}\right]\)
\((C)\) Planck's Constant \((h)\)	\((III)\) \(\left[ M L ^{-1} T ^{-2}\right]\)
\((D)\) Work Function \((\phi)\)	\((IV)\) \(\left[ M L ^2 T ^{-2}\right]\)

Choose the correct answer from the options given below:

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