91Ó°ÊÓ

In what region of space is the potential due to a uniformly charged sphere the same as that of a point charge? In what region does it differ from that of a point charge?

Use the characteristics of the Coulomb force to explain why capacitance should be proportional to the plate area of a capacitor. Similarly, explain why capacitance should be inversely proportional to the separation between plates.

Explain in your own words why equipotential lines and surfaces must be perpendicular to electric field lines.

What is the strength of the electric field in a region where the electric potential is constant?

What is the relationship between voltage and energy? More precisely, what is the relationship between potential difference and electric potential energy?

Can different equipotential lines cross? Explain.

Give the reason why a dielectric material increases capacitance compared with what it would be with air between the plates of a capacitor. What is the independent reason that a dielectric material also allows a greater voltage to be applied to a capacitor? (The dielectric thus increases \(C\) and permits a greater \(V\).)

Voltages are always measured between two points. Why?

(a) Sketch the equipotential lines near a point charge \(+q\). Indicate the direction of increasing potential. (b) Do the same for a point charge \(-3 q\).

The electric field strength between two parallel conducting plates separated by \(4.00 \mathrm{~cm}\) is \(7.50 \times 10^{4} \mathrm{~V} / \mathrm{m}\). (a) What is the potential difference between the plates? (b) The plate with the lowest potential is taken to be at zero volts. What is the potential \(1.00 \mathrm{~cm}\) from that plate (and \(3.00 \mathrm{~cm}\) from the other)?