mm. The device’s capacitance is 1μF. How much charge needs to be transferred
from one plate to the other in order to create a uniform electric field whose strength
is 10^4 V/m?
Solution: Because Q = CV and V = Ed, we find that
Q = CEd = (1 × 10−6)(10^4 )(2 × 10−3) = 2 × 10−5 CExample: A proton (whose mass is m) is placed on top of the positively charged
plate of a parallel-plate capacitor, as shown below.
The charge on the capacitor is Q, and the capacitance is C. If the electric field in
the region between the plates has magnitude E, give an expression that shows the
time required for the proton to move up to the other plate.
Solution: Once we find the acceleration of the proton, we can use Big Five #3,
with v 0 = 0, to find the time it will take for the proton to move the distance y = d.
The acceleration of the proton is F/m, where F = qE is the force the proton feels;
this gives a = qE/m. (We’re ignoring the gravitational force on the proton because it
is so much weaker than the electric force.) Now, since E = V/d and V = Q/C, the
expression becomes a = eQ/mdC. Big Five #3 gives us