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Outline and review

Review on Coulomb's Law and electric field. Discussion about electric potential (energy).

Coulomb’s Law in electrostatics governs the forces between two point charges:

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Review: Coulomb’s Law

While magnitude of the force is calculated using the formula in page 1. The direction of the electric force is given by:

Force is a vector.The direction of the Coulomb force follows1. The line defined by the two point charges.2. Like charges repel, unlike charges attract.

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Review: From Coulomb’s Law to electric field

The concept of a field, here the electric field, is introduced to provide the medium for electric force of one charge to act over a distance and “instantaneously” on another charge.

The definition:

More often used:

F = q · EWhich carries a different meaning: charge in an electric field experiences a force.

testq

FE

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Review: connection of Coulomb’s Law and electric field at point charge level

When e-field of a point charge is concerned:

The direction of the E field is defined by the direction of a positive test charge.

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Review: add up electric fields from charges

E field from multiple point charges:

When the E field is generated by multiple point charges:

A vector sum of E1 to Em, here m is the number of charges.

E field from charges distributed in a volume V:

m

ii

1

EE

V

dEE

2i

ii r

qkE

2i

i r

dvkd

E

with

with

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Review: electric field, field line, force and work

Electric field line is introduced to illustrate the field: Field lines start from positive charge,

end at negative charge. The direction of the force on a positive

test charge is tangent to the field line,

or follow the direction of the field line.

Hence no two field lines cross. The density represents the field strength.

Electric field exerts force on a charge and moves it, doing work on the charge. When the e-field is uniform:

d

UA UB

A B

When a charge q is moved from point A to point B by the E field, the work the electric field does to the charge is:

WAB = Fd = qEd = UA – UB = – (UB – UA ) = – ΔU

i.e., the work the field does equals the negative change of the potential energy of charge q has in the field.

qE

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Review: electric field, field line, force and work

Electric field exerts force on a charge and moves it, doing work on the charge. When the e-field is NOT uniform:

d

UA UB

A B

When a charge q is moved from point A to point B by the E field where the field is a function of the location r, the work the electric field does to the charge is:

The work the field does still equals the negative change of the potential energy of charge q has in the field.

q

E(rA) E(rB)

rA

rB

BA

B

A

AB UUdW rr )(F

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Concepts

Electric potential energy and electric potential inside an electric field: A charge inside an electric field has electric potential energy, like a mass

in a gravitational field has gravitational potential energy. When the charge is a unit positive test charge, the electric potential

energy it possesses equals to the electric potential the field has at that point.

Electric field is a vector field: fields from multiple charges are added together through vector addition.

Electric potential is a scalar: potentials from fields of different charges are added through scalar addition. This is a lot easier than vector addition.

Because electric force is conservative, the work it does to a charge inside the electric field only equals the negative change of the electric potential energy of that charge, has nothing to do with the path the charge took.

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Electric potential from charges

Electric potential from charges: From a point charge:

Q

q

r

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Electric potential from charges

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Electric potential from charges

Electric potential from charges: From multiple point charges:

Q1

r1

Q2

Q3

r2

r3

UA

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Electric potential from charges

Electric potential from charges: From continuous charges:

Charge density ρ,Volume V.

q

r

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Examples

Electric potential from a dipole:

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Examples

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Examples

Electric potential from a charge disk:

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Examples

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Potential and potential difference

Like in gravitational potential, the absolute electric potential is meaning less unless a reference point is specified.

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Electric potential and electric field

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example

A region of space has an electric potential described by the equationV(x, y, z) = xyz. Find an expression for the electric field vector in the region.