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Potential Energy due to Úniform Electric Field Consider the 1D motion of a charge

`q>0`

along with the vertically down uniform electric field

`E=-|E|<0`

generated by a pair of charged parallel plates. Choosing up as the positive direction, let

`h_(+)`

be the height of the positively charged plate and

`h_(-)`

be the negatively charged plate such that

`h_(+)>h_(-)`

. For the time being, we ignore gravity. (a) Let

`h`

be in

`h_(-)<=h<=h_(+)`

. At the height

`h`

, draw a free-body diagram. (b) The direction of the electrostatic force is downward. Let us define the distance traveled

`d:=h_(-)-h_(+)<0`

, from

`h_(+)`

to

`h_(-)`

. Calculate the total work

`W`

done by electrostatic force force along with

`d`

. (c) Choose a correct statement: 1)

`W>0,2`

. (d) Find a relation among

`K_(+-),W`

, applying the Work-Energy Theorem, where

`K_(+-)`

stands for the kinetic energy of

`q`

at

`+-`

-plate. (e) If it is under the uniform gravity

`g=-|g|<0`

, as well as electric field

`E`

, how do we modify the above result? Now, suppose the gravity is negligible. (f) The associated potential energy provides the work

`W`

. If

`U_(+-)`

are the potential energies at

`h_(+-)`

, i.e., at

`+-`

-plate, find a relation among

`U_(+-),W`

. (g) If we choose the voltage of the lower plate

`V_(0)`

, relative to the earth, how much is the electric potential of the upper plate? Note that electric potential is the potential energy per unit charge.