4/24/15oregon state university ph 213, class #121 summary of electrostatics field“payload”effect...

4/24/15 Oregon State University PH 213, Class #12 1

Summary of Electrostatics

Field “payload” Effect

E · q = F

E = –dV/ds F = –dUE/ds

V · q = UE


The Voltage Difference Created bya Set of Parallel Plates

Since the E-field between two plates is a constant, it’s easy to find the work necessary to move a charge against that field (just like moving a mass against a constant local g) for a distance d:

W = UE = qEd

So the potential difference (also called the voltage difference) magnitude is V = UE/q = Ed

But you are moving a displacement d against the field to increase voltage: V = UE/q = –Ed

So in general (not just between plates): E = –dV/ds, where ds is an incremental distance moved along the direction of E.

A capacitor is essentially a pair of parallel, oppositely-charged conductive plates.

The electric potential inside a capacitor…

1. is constant 2. increases linearly from the negative to the positive

plate 3. decreases linearly from the negative to the

positive plate 4. decreases inversely with distance from the

negative plate 5. decreases inversely with the square of the distance

from the negative plate4/24/15 3Oregon State University PH 213, Class #12

The electric potential inside a capacitor

1. is constant 2. increases linearly from the negative to

the positive plate 3. decreases linearly from the negative to

the positive plate 4. decreases inversely with distance from

the negative plate 5. decreases inversely with the square of

the distance from the negative plate

4/24/15 4Oregon State University PH 213, Class #12

Rank in order, from largest to smallest, the potentials Va to Ve at the points a to e.

1. Vd = Ve > Vc > Va = Vb

2. Vb = Vc = Ve > Va = Vd

3. Va = Vb = Vc = Vd = Ve

4. Va = Vb > Vc > Vd = Ve

5. Va = Vb = Vd = Ve > Vc


Which electric potential graph describes this

electric field?



Summary of Electrostatics

Field “payload” Effect

E · q = F

E = –dV/ds F = –dUE/ds

V · q = UE


The Strength of the Electric Potential Field(Voltage) Created by a Point Charge

Q: It’s all well and good to look at simple, uniform electrical fields between parallel charged plates, but what about when the fields are not uniform—such as when point charges create them? What is the electric potential (voltage) at any point in space due to a nearby point charge, q?

A: V = kq/r, where r is the distance from q to the point in question. This is a result of integrating Again, the sign of the charge again indicates how the potential changes in the space around it.

Note where we have selected V = zero only at an infinite distance from q. (The analogy to gravity goes on.)

Rank in order, from largest to smallest, the potential energies Ua to Ud of these four pairs of charges. Each + symbol represents the same amount of charge.

A. Ua = Ub > Uc = Ud B. Ub = Ud > Ua = Uc C. Ua = Uc > Ub = Ud D. Ud > Uc > Ub > Ua E. Ud > Ub = Uc > Ua


Rank in order, from largest to smallest, the electric potentials (“voltages”) of these four collections of charge [measured at the midpoint between them]. Each + symbol represents the same amount of charge.


[Voltage is a field—a description of a certain property—of a point in space, so we must specify that point.]

4/24/15oregon state university ph 213, class #121 summary of electrostatics field“payload”effect...

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