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This course includes Motion, Oscillations, waves and propagation, Electric Charge and Coulomb Law, Electric Field, Electric Potential, Capacitors and Dielectric, Current and Resistance, AC and DC, Magnetic fields, Ampere Law and Faraday law, Maxwell equations and Traveling waves. This file includes: Electrostatic, Gravitational, Force, Electric, Potential, Point, Charges, Field, Vector, Energy, Forces
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Electric Potential Electrostatic and Gravitational force
Electric Potential Energy (EPE)
Electric Potential
Potential due to Point Charges
Calculating the Potential from the Field
Calculating the Field from Potential
Equipotential Surface
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Introduction
Force is a vector and energy is scalar
In problem involving vector forces and fields
Calculations require sums and integral are often completed
In this chapter we will study
The energy method for electrostatics field
we will start with the electric potential energy
It is a scalar and will characterize an electrostatic force
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The difference in potential energy between two points is equal to the negative of Work done by a force ΔU = - Wab
Above equation is possible only for conservative forces Which means that potential energy can only be defined for conservative forces
Forces are conservative if and only if the work done by these forces when a body moves from a to b is independent of the path taken between these two locations
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For example work done by a force in the gravitational field is independent of the path followed by the particle
III
b
a II
We can make a similar argument for the electrostatic force with the same result
Which means that the electrostatic force is also conservative and can be demonstrated by potential energy
The only difference between the two is that gravitational force is only attractive and electrostatic force can be attractive and repulsive both
7
Consider system of two positive charges +q and q 0
The charge q 0 moves under the influence of E field created by +q
The charge q 0 moves a small displacement dr as it moves from position A to position B
Electric Potential Energy +++++++++++++ q
qo
A qo
rB Δr
rA
8
+++++++++++++ q
qo
A qo
rB Δr
rA
Magnitude of E field created by +q decreases as the charge q 0 moves farther away from charge +q
The charge q 0 experiences a force (F = q 0 E ) that varies with displacement
We need to calculate work done by a variable force
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Work done by F = q 0 E WAB = EPEA – EPEB
+q rA A
B F = q 0 E
q 0
q 0
F = q 0 E
+++++++++++++
rB
Electric Potential Energy
A B
AB
B
A
B
A
AB
= (^0) 2 = 0 1
A B
AB
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Work done by F = q 0 E WAB = EPEA – EPEB
+q rA q 0
q 0
+++++++++++++
rB
Note that the above work must be related to change in Electric Potential Energy
Electric Potential Energy
A B
AB
F = q 0 E
AB B A
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Work done by F = q 0 E WAB = EPEA – EPEB
+q rA A
B F = q 0 E
q 0
q 0
F = q 0 E
+++++++++++++
In the above equation rA rB is the initial separation between the charges and rB is the final separation
Electric Potential Energy
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Electric Potential Energy
+++++++++++++^ +q Let us assume that the charge q 0 was at an infinite distance from this system
rintial =
0
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+q q 0
q 0
+++++++++++++
The EPE is only depend upon the^ r distance between the two positive charges and will be different if we place q 0 at different separation r
Remember that EPE is a scalar quantity
Where is the magnitude of E Also field at a distance r from q
Electric Potential Energy
(1) r
kq U(r)
q = 0
U =^ r E q 0 E
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(1) r
kqq U(r) =^
0
If the electric force is attractive, q and qo have opposite signs, and so the product qqo is negative, the electric potential energy given in equation will be negative
If the electric force is repulsive, q and qo have the same sign, and the product qqo is positive, the electric potential energy is positive.
If we move qo toward q (source charge) from an initially infinite separation, the potential energy increases from its initial value, which we have consider as zero.
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Now we bring another charge q 2 from infinity
q (^1) r q 2 12
Electric Potential Energy of a System of Charges
12
1 2 r
kq q U =
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And now we bring another charge q 3 from
infinity q 3
q 1 q 2
r 23
r 13
r 12
Electric Potential Energy of a System of Charges
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2 3
13
1 3
12
1 2 r
kq q
r
kq q
r
kq q U = + +
