a2 h 43 electricfields
TRANSCRIPT
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Electric force
This is the ATTRACTIVE or REPULSIVE forceexerted between objects due to theirCHARGE
LIKE charges REPEL;UNLIKE charges ATTRACT
(UNLIKE includes the case where one object isuncharged)
CHARGE is measured in COULOMBS (C)
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Electric fields
These are regions withinwhich an object
experiences electric force.
They can be representedby lines of force.
Arrows show the
direction of the force on
a POSITIVE charge.
Line density increases
with the strength of the
field.
test positive charge
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Radial electrical fields
These exist around pointcharges.
The field around a uniformsphere is also radial.
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Some other field patterns
Draw the pattern expected for twolike positive charges add somearrows to show the field direction.
X
neutral point
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Field between parallel plates
+ + + + + + +
- - - - - - -
Electric field is
uniform in thecentral region
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Electric field strength (E )
This is equal to the force per very small positive unittest charge.
Definition: E = force E = F
charge q
unit of E: N C -1
VECTOR:Direction the same as the force on a POSITIVE charge.
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Force / N Charge E / NC-1
12 3 C
25 0.5
6 C 8
500 C 20
9 m 300 C
20 40
0.5 n 500 pC
Complete:
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Coulombs law
The force between two point charges is:1. directly proportional to the product of
the charges
2. inversely proportional to the square of
their distance apart
3. maximum when the charges are separated
by a vacuum
Coulombs law is the electric field equivalent of Newtons law of
gravitation.
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Mathematically: F Q1Q2r2
Q1and Q2are the charges, ris the distance apart
Inserting a constant of proportionality:
F = 1 Q1Q2
4o r2
ois called the permittivity of free space.
o= 8.85 x 10-12 C 2N -1m -2.
The permittivity of air is usually taken to be the same as a vacuum freespace.
The permittivity of other media, especially insulators, is higher.The unit of permittivity is more usually F m -1(farad per metre) wherethe farad is the unit of capacitance (to be covered later).
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Question
Calculate the electrostatic force of attraction between the
proton and electron inside an atom of hydrogen.
Charge of a proton = + 1.6 x 10 19C
Charge of an electron = - 1.6 x 1019
CDistance apart = 5.0 x 10 11m
o= 8.85 x 10-12 C 2N -1m -2
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Gravity Comparison Question
Calculate the gravitational force of attraction between theproton and electron inside an atom of hydrogen andcompare your answer with the previous question.
Mass of a proton = 1.67 x 10 27kg
Mass of an electron = 9.11 x 10 31kgDistance apart = 5.0 x 10 11m
G= 6.672 x 10 -11N m 2kg - 2.
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Radial field relationship between Eand o
E = F / qwhere qis a very small positive test charge feeling theelectric force of a much greater charge Q
Coulombs law in this situation can now be written:
F = 1 Q q4o r
2
Substituting Ffrom the 2ndequation into the 1st:
E = 1 Q q
4
o r
2
qE = Q i
4o r2
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QuestionCalculate the electrical field strength:
(a) 2 cm away from a point charge of + 5 C
(b) 4 cm away from a point charge of - 10 Co= 8.85 x 10
-12 C 2N -1m -2
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Electrical potential (V )
The electrical potential of a point within an electric
field is equal to the work that must be done per
coulomb of POSITIVE charge in bringing the charge
from infinity to the point.
Notes:
1. The electrical potential at infinity is ZERO.
2. Points around positive charges usually (but not always) havepositive potentials and vice-versa.
3. Electrical potential is measured injoules per coulomb (J C-1
) ormore commonly volts(V) where 1V equals 1 JC-1.
4. Electrical potential is a SCALARquantity
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Electrical equipotentials
These are surfaces thatjoin up points of equal
potential.
No work is done byelectrical force when a
charge is moved along an
equipotential surface.
Equipotentials are always
perpendicular to field
lines.
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Variation of Eand Vabout a positive charged
sphere of charge Qand radius ro
E = Q i
4o r2
V = Q i
4o r
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Combining fields question
Calculate the resultant force, electric
field strength and electrical potentialexperienced by test charge + q ofmagnitude 2pC in the situationsshown opposite.
Both Q1& Q2have a charge of
magnitude of 4C
In situations (a) and (b) q is 3cm fromQ1and 4cm from Q2In situation (c) q is 4cm from Q1and3cm from Q2
Remember that both force and electricfield strength are vectors but thatelectrical potential is a scalar.
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Electrical potential
difference (V )
When a charge, Qis moved through an
electrical potential difference of Vthe
work done Wis given by:
W = Q x V
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Question 1
Calculate the work required to move acharge 40 mC between two electrodes of
potential difference 5 kV.
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Question 2
Calculate the work required to move anelectron of charge 1.6 x 10 -19C between two
electrodes of potential difference 1V.
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Potential gradient in a uniform
electric field (V / d)
This is the change in potentialper metre at a point within anelectrical field.
po tential gradient = V
dunit: J C-1m-1
or more usually: V m-1
E = V
d
Electric field strength is alsomore commonly measured inV m -1
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Question 1
Calculate the electric field strength betweentwo parallel electrodes separated by 2.0 mm
and a potential difference of 60V.
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Question 2
Estimate the potentialdifference between the base
of a thundercloud and the
ground if they are separated
by 500m and if an electricfield of 12 kV m -1is required
for a lightning stroke.
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Comparison of electric and
gravitational fields
Similarities: Differences: