FOCUS ON
ELECTRIC
POTENTIAL
AP PHYSICS B
KERNION
MAIN POINTS
oElectrical Potential Energy (UE), scalar quantity depends on:
o position in the E-field
o amount of charge
o magnitude of the E-field at that point
o For uniform E-fields:
o ΔU = -qEd for a positive charge moving ALONG the field
o ΔU = qEd for a negative charge moving ALONG the field
oA new scalar quantity, Electric potential (V) is defined as the
electric potential energy per unit charge
o U/q = V (You MUST use the sign on q)
o ΔU/q = ΔV (The change in electric potential...voltage)
o unit = J/C = volt (v)
FOR MOVEMENT ALONG
A UNIFORM E-FIELD
oFor a positive charge
o ΔU/q = ΔV = -qEd/q = -Ed
oFor a negative charge
o ΔU/q = ΔV = qEd/-q = -Ed
oMovement ALONG the field ALWAYS lowers the electrical
potential
oN/C = V/m
EXAMPLE
oA proton is released from rest in a uniform E-field (E = 8 x
104 V/m) directed to the right. The proton moves a distance
of 0.5 m along the field. Find the following quantities
o ΔV, ΔU, ΔK, v, WE
o ΔV = -Ed = (8x104)(0.5) = 4x104 volts
o ΔU = q ΔV = 1.6x10-19C (4x104 v) = 6.4x10-15J
o ΔK = -ΔU = -6.4x10-15 J = ½ mv2 = ½(1.67x10-27kg)
o v = 2.8x106m/s
o WE = - ΔU = ΔK = -6.4x10-15 J
ELECTRIC POTENTIAL AND
NON-UNIFORM E-FIELDS
+
Electric potential caused by a point particle
V = kq/r (keep sign on charge)
EXAMPLE PROBLEM
Find the electric potential at point p
p
4m
3m
q1
q2
(0.5 μC)
(-2.0 μC)
VP = ∑kq/r = k[q1/r1 + q2/r2]
VP = 9x109[(0.5x10-6/4) + (-2x10-6/5)
VP = -2475 volts