Potential Energy of a system of charges - Physics Courses
嚜燕otential Energy of a system of charges
+
+
+
+
+
+
+
+q
d
F = qE
+q
_
_
_
_
Potential Energy PE (scalar):
忖PE = 每 Work done by the Electric
field
忖PE= 每W= 每 Fd= 每 qEd
_
_
_
(units = J)
Work done by the E-field (to move the +q closer to the negative plate)
REDUCES the P.E. of the system
If a positive charge is moved AGAINST an E-field (which points from
+ to -), the charge-field system gains Pot. Energy. If a negative
charge is moved against an E-field, the system loses potential energy
Electric Potential Difference, 忖V
忖V = VB 每 VA = 忖PE / q
+
+
+
+
+q
Units: Joule/Coulomb = VOLT
Scalar quantity
+
+
+
Point A
d
+q Point B
Relation between 忖V and E:
忖V = Ed
E has units of V/m = N/C
(V / m = J / Cm = Nm / Cm = N / C)
_
_
_
_
_
_
_
Potential vs. Potential Energy
POTENTIAL: Property of space
due to charges; depends only on
location
Positive charges will accelerate
towards regions of low potential.
+
+
+
+
+
+
+
POTENTIAL ENERGY:
due to the interaction
between the charge and
the electric field
+
+
+
V1
+
+
+
+
+q
PE1
+q
PE2
忖PE
忖V
V2
_
_
_
_
_
_
_
_
_
_
_
_
_
_
Example of Potential Difference
A parallel plate capacitor has a constant electric
field of 500 N/C; the plates are separated by a
distance of 2 cm. Find the potential difference
between the two plates.
+
+
+
忖V
_
+
+
+
+
E-field is uniform, so we can use
忖V = Ed = (500V/m)(0.02m) = 10V
d
_
_
_
_
_
_
Remember: potential
difference 忖V does not
depend on the presence of
any test charge in the E-field!
Example of Potential Difference
Now that we＊ve found the potential difference 忖V, let＊s take a
molecular ion, CO2+ (mass = 7.3℅10每26 kg), and release it from
rest at the anode (positive plate). What＊s the ion＊s final velocity
when it reaches the cathode (negative plate)?
Solution: Use conservation of energy: 忖PE = 忖KE
+
+
+
+
+
+
+
忖PE
_
_
_
忖PE = 忖V q
忖KE = 1/2 m vfinal2 每 1/2 m vinit2
忖V q = 1/2 m vfinal2
_
_
_
_
vfinal2 = 2忖Vq/m = (2)(10V)(1.6℅10每19C)/7.3℅10每26 kg
vfinal = 6.6℅103 m/s
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