Electric Potential and Energy Questions and Answers

Answer: C

For a uniform field the magnitude is the potential difference divided by the separation, \( 200/0.002 = 10^{5} \) V/m. The result is close to the breakdown strength of many gases, which is why capacitor spacings are chosen with care.

Answer: D

Correct answer: False, the interior of a charged conductor having zero field at finite potential

The field is the gradient of the potential, so a zero field means the potential is not changing, not that it is zero. The inside of a charged conductor is the standard counterexample: no field anywhere within it, and the whole body at whatever potential its charge gives it.

Answer: A

The midpoint between equal and opposite charges is at zero potential and has a field of twice the contribution of either charge. The two statements about field and potential are independent of one another in both directions.

Answer: B

Correct answer: False, the interior sitting at the same potential as the shell itself

Zero field within means constant potential within, and continuity at the surface fixes that constant at the shell’s own value. The interior would be at zero only if the shell were earthed, which is a different arrangement.

Answer: C

Correct answer: both the assertion and the reason are true and the reason explains the assertion

Both are true and the reason gives the mechanism. Zero work along the surface means \( \mathbf{E}\cdot d\mathbf{l} = 0 \) for every displacement lying in it, which requires the field to have no component in the surface - that is, to be normal to it everywhere.

Answer: D

Integrating an inverse first power field gives a logarithm, which grows without bound, so infinity cannot serve as a reference. Had the field fallen as the inverse square the integral would have converged, as it does for a point charge.

Answer: A

Correct answer: both the assertion and the reason are true and the reason explains the assertion

Both are true and the reason gives the mechanism. Because the charges attract, the field does the work of bringing them together and energy is released to the surroundings. The potential energy of the pair is correspondingly negative, which is what it means for the pair to be bound.

Answer: B

Each differentiation with respect to distance steepens the fall by one power, and the energy density goes as the square of the field. The pattern one, two, four is worth remembering as a set rather than as three separate facts.

Answer: C

Correct answer: 1-R, 2-P, 3-Q

Potential is a scalar, so contributions simply add with their signs. At the midpoint of two like charges the two positive contributions add to twice either one. At the midpoint of two opposite charges they cancel to zero - though the field there is not zero, the two field vectors pointing the same way. And inside a hollow conductor the potential holds its surface value.

Answer: D

The scalar integration comes first because it is the easy step, and the differentiation is left to the end when a single function of position is available. Doing it the other way round means integrating vectors, which is the harder route.