Download electric fields

SPH4U1 – FIELDS – L4 Electric Potential
ELECTRIC POTENTIAL
Electric Potential energy can be defined as the energy stored in a system of two
charges a distance r apart. Deriving the formula can be a little tricky, but making
assumptions based on the close relation between the interaction of charges and the
interaction of masses will make it easier. Keep in mind that the close relation does not
imply that the forces are identical. The main difference is that gravity is always attractive
and electricity can either attract or repel.
Let’s start with what we know about the force of gravity, gravitational potential energy
and Coulomb’s Law and work from there.
KNOWN FORMULAS:
Fg 
Gm1 m2
r
2
, Fg  mg , E g  mgh , FE 
kq1 q 2
r2
FINDING EE (Electrical Potential Energy):
SIGN CONVENTION: If the charges are the same, than the electric potential is positive,
which makes intuitive sense. If the charges are opposite however, we get a NEGATIVE
potential energy. What does this mean? How can you have negative potential? It is
really a matter of “relativity”. It is only negative “relative” to some point (let’s call it the
zero level of electric potential). Let’s use a gravitational comparison to help us
understand this. We usually think of (gravitational) potential energy at the earth's
surface to be zero. If we raise an object we consider it to have gained potential energy
because we did work against the force of gravity. But dig a hole on the beach and move
the object into it and it's now at negative potential to where it was at the earth’s surface.
It's all relative.
SPH4U1 – FIELDS – L4 Electric Potential
We must consider electric potential energy on a broader spectrum. By this, I mean that
we must consider the electric potential as the amount of energy per unit of charge.
Electrical Potential Energy (EE) is different from Electric Potential (V). Recall from last year,
that electric potential is represented by a V and is more commonly called Voltage. The
units are in J/C.
EE
q
kq1 q
V r
q
kq
V 1
r
V
The exact definition of electric potential is as follows:
1 V is the electric potential at a point in an electric field IF 1 J of work is required to
move 1 C of charge from infinity to that point.
ELECTRIC POTENTIAL DIFFERENCE:
If we are moving a test charge from one point in a field (point A) to another point in a
field (point B), then we are dealing with a difference in electric potential between these
two points. In this case, the difference between electric potential will be equal to the
work per unit charge that we would perform in order to move this hypothetical test
charge.
Mathematically,
EB  E A  W
qVB  qV A  E E
q (VB  V A )  E E
qV  E E
SPH4U1 – FIELDS – L4 Electric Potential
What about the electric potential difference between two plates?
A
B

FE
Recall  
and W  E  Fd . From these, we can derive an expression for the
q

magnitude of the electric field at any point in the space between the two parallel plates.
EX 1: Calculate the electric potential at a distance of 0.40m from a spherical point charge
of 6.4 x 10-6 C.
SPH4U1 – FIELDS – L4 Electric Potential
EX 2: How much work must be done to increase the potential of a charge of 3.0 x 10-7C
by 120V?
EX 3: The magnitude of the electric field strength between two parallel plates is 450 N/C.
The plates are connected to a battery with an electric potential difference of 95V. What
is the plate separation?
HMWK: Pg. 354 #1-4 Pg. 358 #7,8
SPH4U1 – FIELDS – L4 Electric Potential
ASSIGNMENT PROBLEMS:
1. Charged spheres X and Y are in a set position and have charges
, respectively. Calculate the net force on sphere Z, of charge
and
.
2. Point charges W, X, Y, and Z each have the same magnitude charge of
. Two
of the charges are positive and two are negative, each at opposite corners. The corners
of the square are 10.0 cm long. Calculate the net force on each of the point charges.
Draw vector diagrams for each point charge.
3. Two charges, one of charge +2.5 x 10–5 C and the other of charge –3.7 x 10–7 C, are 25.0
cm apart. The positive charge is to the left of the negative charge.
(a) Draw a diagram showing the point charges and label a point Y that is 10.0 cm away
from the negative charge, on the line connecting the charge. (Field lines do not need to
be drawn.)
(b) Calculate the electric field at point Y.
4. (a) What is the electric potential from a charge of 3.0 x 10–5 C at 15 cm and 65 cm?
(b) How much work must be done to carry a +2.3 x 10–3 C charge from 65 cm to 15 cm?