CHAPTER 10 DRILL
- E A counterexample for I is provided by two equal positive charges; at
the point midway between the charges, the electric field is zero, but the
potential is not. A counter-example for II is provided by an electric dipole (a
pair of equal but opposite charges); at the point midway between the charges,
the electric potential is zero, but the electric field is not. As for III, consider a
single positive point charge +Q. Then at a distance r from this source charge,
the electric field strength is E = and the potential is V =. Thus, V =
rE, so V is not inversely proportional to E.
- A At the center of the square, the electric fields would all cancel. The
contribution from the upper-left charge would point away from it, towards
the lower-right charge, but the contribution from the lower-right charge
would point exactly the opposite direction and cancel it. Likewise, the
contributions from the lower-left and upper-right charges would cancel.
- E The electric potential due to any one of the charges is , where
, since the distance from the charge to the center has that value. (To show this,
draw a right triangle, the hypotenuse of which is the line from the center of the
square to a charge. You’ll have a base and a height of length s/2.) That is, the
potential due to one charge is. The potential due to four charges is just
four times that potential, since electric potentials are scalars and just add
together if they are all positive, so the total is.
- B A negative charge moves from an area of low electric potential to an area of
high electric potential.
- C Both electric force and electric field obey inverse square laws. The
equation for electric force is F = , and the equation for electric field is
