True or false on field and potential

True or false?

1. Electric field lines go from positive charges to negative charges.
2. In electrostatic equilibrium, the field inside a conductor is zero.
3. Equipotential surfaces coincide with field lines.
4. A positive charge moves spontaneously towards points of lower potential.
5. The potential generated by a point charge decreases as $1/r^2$.

Solution

$\ev{\text{V, \ V, \ F, \ V, \ F}}$

1) True. By convention field lines emerge from positive charges (sources) and enter negative charges (sinks). The direction of the line indicates the direction of the force on a positive test charge.

2) True. In electrostatic equilibrium the free charges of a conductor redistribute themselves until the internal field vanishes: if a field remained, the charges would keep moving, contradicting equilibrium. All the excess charge arranges itself on the surface.

3) False. Equipotential surfaces are perpendicular to field lines, not coincident. Along a field line the potential varies (work is done), while on an equipotential it is constant.

4) True. A positive charge is pushed by the force $\vv{F} = q\vv{E}$ towards decreasing potentials, i.e. it “descends” the potential like a mass falling in the gravitational field. A negative charge would do the opposite, rising towards higher potentials.

5) False. The potential of a point charge decreases as $1/r$: $V = \frac{kQ}{r}$ It is the field that decreases as $1/r^2$. Confusing the two dependences is a common mistake.

Links

Topics: Electric field and potential Concepts: Electric field · Electric potential · Conductors in electrostatic equilibrium Skills: Superposition principle Methods: Gradient method Objects: Charged sphere