electric field-intro electric force is a field force. field forces can act through space, i.e....
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Electric Field-IntroElectric force is a field force.Field forces can act through space, i.e.
requires no physical contact. Faraday developed the concept of a field in
terms of electric fields
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Electric Field-DefinitionAn electric field is said to exist in the region
of space around a charged objectThis charged object is the source charge
When another charged object, the test charge, enters this electric field, an electric force acts on it.
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Electric Field – Definition, contThe electric field is defined as the electric
force on the test charge per unit charge.The electric field vector, , at a point in
space is defined as the electric force acting on a positive test charge, qo placed at that point divided by the test charge:
E
F
oqF
E
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Electric Field-NotesThe existence of an electric field is a property
of the source chargeThe presence of the test charge is not necessary for
the field to exist
The test charge serves as a detector of the field
The direction of is that of the force on a positive test charge
The SI units of are N/C
E
E
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Relationship Between F and E If q is placed in electric field , then we have
This is valid for a point charge only For larger objects, the field may vary over the size
of the object
If q is positive, the force and the field are in the same direction
If q is negative, the force and the field are in opposite directions
e qF E
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Electric Field, Vector FormFrom Coulomb’s law, force between the
source and test charges, can be expressed as
Then, the electric field will be
2ˆo
e e
qqkr
F r
2ˆe
eo
qk
q r F
E r
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Superposition with Electric FieldsAt any point P, the total electric field due to a
group of source charges equals the vector sum of the electric fields of all the charges
2ˆi
e ii i
qk
r E r
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Superposition ExampleFind the total at E
P
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Electric Field – Continuous Charge DistributionPoint charge – charge
with zero sizeContinuous charge –
object with charge distribution
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Electric Field – Continuous Charge Distribution, equationsFor the individual charge
elements
Because the charge distribution is continuous
2ˆ
e
qkr
E r
2 20ˆ ˆlim
i
ie i eq
i i
q dqk k
r r
E r r
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Amount of Charge in a Small VolumeIf the charge is uniformly distributed over a
volume, surface, or line, the amount of charge, dq, is given byFor the volume: dq = ρ dVFor the surface: dq = σ dAFor the length element: dq = λ dℓ
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Charge DensitiesVolume charge density: when a charge is
distributed evenly throughout a volumeρ ≡ Q / V with units C/m3
Surface charge density: when a charge is distributed evenly over a surface areaσ ≡ Q / A with units C/m2
Linear charge density: when a charge is distributed along a lineλ ≡ Q / ℓ with units C/m
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Example – Charged DiskFind and point E
P
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Electric Field LinesField lines help us to visualize the electric
fieldThe electric field vector is tangent to the
electric field line at each point
The number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that region
E
PPE
electric field line
electric field lines
P QPE
QE
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Electric Field Lines, Positive and Negative Point ChargeThe field lines
radiate outward from positive charge in all directions
The field lines radiate inward from positive charge in all directions
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Motion of Charged ParticlesWhen a charged particle is placed in an
electric field, it experiences an electrical force
The net force will cause the particle to accelerate according to Newton’s second law
If is uniform, then the acceleration is
constant
e q m F E a
E
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Electron in a Uniform Field, ExampleThe electron is projected horizontally into a
uniform electric field