E =. Thus, both of these would be one-quarter as great at twice the
distance. However, electric potential is just an inverse. The equation for
electric potential is φ = (notice that the r is not squared). Thus, at twice
the distance, it would be half as great. Thus, only Roman numeral III is true.
- C Remember, electric field and electric potential are two different things.
Because E is uniform, the potential varies linearly with distance from either
plate (∆V = Ed). Since points 2 and 4 are at the same distance from the
plates, they lie on the same equipotential. (The equipotentials in this case are
planes parallel to the capacitor plates.)
- D As we move from point A to point B, the potential decreases by 10 V, so ∆V
= −10 V. Now, since ∆U = q∆V, we have ∆U = (−2 C)(−10 V) = +20 J.
- A Since Q cannot change and C is increased (because of the dielectric),
∆V = Q/C must decrease. Also, since UE = , an increase in C with no
change in Q implies a decrease in UE.
- B By definition, WE = −∆U =−q∆V, which gives
WE = −q(VA − VB) = −(−0.05 C)(200 V − 100 V) = 5 J
Notice that neither the length of the segment AB nor that of the
curved path from A to B is relevant.
