Electric Potential and Energy Questions and Answers

Answer: A

Correct answer: a charge from one point to the other against the field

\[ V_{ab} = -\int_b^a \mathbf{E}\cdot d\mathbf{l}. \] The work is per unit charge, so the result is a property of the field and the two points rather than of the charge moved. Moving round a closed path returns zero, which is the same statement that makes the field conservative.

Answer: B

Correct answer: infinity, where the potential is taken as zero

Only differences in potential have physical meaning, so a reference must be chosen. Infinity is the natural choice for an isolated charge distribution, since the field vanishes there. In circuit work the earth or a chassis is used instead, and the choice is a convention rather than a fact about nature.

Answer: C

Integrating the inverse square field inward from infinity yields an inverse first power potential. The distinction between the two powers is worth fixing firmly, since confusing them is the commonest error in electrostatics.

Answer: D

Signs must be respected but no directions are involved, which makes the potential far easier to compute than the field for an assembly of charges. The field can then be recovered as the negative gradient of that potential.

Answer: A

The minus sign makes the field point from high potential to low, which is the direction a positive charge is pushed. The magnitude of the field is the greatest rate of change of potential with distance, which is why volts per metre is its unit.

Answer: B

Moving a charge along such a surface requires no work, which means the field can have no component along it. The field is therefore everywhere normal to an equipotential, and the surface of a conductor in equilibrium is one.

Answer: C

Correct answer: any potential difference along it would drive a surface current

In equilibrium no current flows, so no potential difference can exist between any two points of the conductor. The whole body, surface included, is therefore at one potential - and it follows that the external field must meet the surface at right angles, since a tangential component would imply a difference along it.

Answer: D

Correct answer: the two end points only

The electrostatic field is conservative, so the line integral between two points is the same along every path and the work depends only on where the charge starts and finishes. That path independence is exactly what allows a potential function to be defined at all.

Answer: A

Integrating the inverse first power field gives a logarithm, which diverges at infinity, so a reference at some finite radius must be chosen instead. The potential difference between two radii remains perfectly well defined.

Answer: B

Correct answer: constant and equal to its surface value

The field inside the shell is zero, so no work is done moving a charge anywhere within it and the potential cannot change - it holds the value it has at the surface. Zero field means constant potential, not zero potential, which is the distinction this item exists to make.