a2 h 43 electricfields

8/12/2019 a2 h 43 Electricfields

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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:

a2 h 43 electricfields

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