Force between Two Point Charges

1
Force between Two Point Charges

• The force between two point charges is
• directly proportional to the magnitude of each
  charge (q1, q2),
• inversely proportional to the square of the
  separation between their centers (r),
• directed along the line connecting their centres.
  

2
Coulombs Law

• Coulomb's law describes the force between two
  charged particles.

For a vacuum
Where ?o is called the permittivity of free space
and ?o 8.85 10-12 F m-1
And also
3
Electric Fields
http//www.colorado.edu/physics/2000/applets/nforc
efield.html

• The space around a charged body, where electric
  force is experienced by a test charge, is called
  an electric field.

• By a test charge we mean a charge so small that
  the force it exerts does not significantly alter
  the distribution of the charges that create the
  field.

4
Electric Field Lines

• The electric field lines indicate the direction
  of the force due to the given field on a positive
  test charge.
• The field points in the direction tangent to the
  field line at any point.
• The number of field lines drawn per unit
  cross-sectional area is proportional to the
  electric field strength.

F
5
Properties of Field Lines
http//surendranath.tripod.com/FieldLines/FieldLin
es.html

• Electric field lines start on positive charges
  and end on negative charges.
• The number starting or ending is proportional to
  the magnitude of charge.

• The field lines cannot cross.
• The closer the lines the stronger the field.
• Where the lines are parallel and uniform spaced,
  the field is uniform.

6
Electric Field Patterns (1)

• Electric field lines for a single negative point
  charge

• Electric field lines for a single positive point
  charge

7
Electric Field Patterns (2)

• Electric field lines for two charges of opposite
  sign.

• Electric field lines for two equal positive
  charges

8
Electric Field Patterns (3)

• Electric field lines between two oppositely
  charged parallel plates.

9
Electric Field Strength

• The electric field strength , E, at any point in
  an electric field is defined as the force per
  unit charge exerted on a tiny positive test
  charge at that point.

Unit N C-1 or V m-1

• E represents a vector quantity whose direction is
  that of the force that would be experienced by a
  positive test charge.
• The magnitude of q must be small enough not to
  affect the distribution of the charges that are
  responsible for E.

10
Electric Field Strength due to a Point Charge

• By Coulombs law

• By the definition of E

Then we have
Notice that E depends only on Q which produces
the field, and not on the value of the test
charge q.
11
Vector Addition of Electric Field

• Suppose we have several point charges Q1, Q2 and
  Q3 etc. Then we can
• Evaluate E1, E2 and E3 etc., and
• Find E ?Ei by using vector addition.

12
Electric Field and Conductor

• Any net charge on a good conductor distributes
  itself on the surface.
• E is always perpendicular to the surface outside
  of the conductor. (i.e. E has no component
  parallel to the surface.)
• E is zero within a good conductor.

If the charge are kept moving, as in current,
these properties need not apply
13
Electric Field due to a Charged Spherical
Conductor

• Inside the sphere
• The electric field is zero.
• Outside the sphere
• For r ? a

• On the surface of the sphere

Where ? is the surface charge density.
14
Electric Field due to a Non-conducting Charged
Sphere

• Inside a non-conductor, which does not have free
  electrons, an electric field can exist.
• The electric field outside a nonconductor need
  not to be perpendicular to the surface.

15
Electric Potential Energy

• The Coulomb force is a conservative force (i.e.
  The work done by it on a particle which moves
  around a closed path returning to its initial
  position is zero.)
• Therefore, a particle moving under the influence
  of a Coulomb force is said to have an electric
  potential energy defined by
• U qV

16
Electric Potential Energy of a System

• Consider an electric field formed by a system of
  N charges.
• Work has to be done to assemble the charges from
  infinity in their final positions.
• The electric potential energy of the field is
  defined to be the algebraic sum of the electric
  potential energy for every pair of charges.

17
Electric Potential

• Electric potential is a measure of the electrical
  potential energy per unit charge at a point in an
  electric field.
• The electric potential at a point in an electric
  field is the work done in moving a unit positive
  charge from infinity to that point.

Unit volts (V)

• Electric potential is a scalar quantity.

18
Field Strength and Potential Gradient
http//www.falstad.com/vector2de/

• The work done by a force F to move the test
  charge q against the electric force by a small
  distance ?r is

and
As
We get
Hence
for ?r? 0
i.e. Electric field strength -potential gradient
19
Electric Potential due to a Point Charge

• In terms of the E-field, the electric potential
  is defined by

The - sign indicates that work is done against
the electric force.

• For the electric field due to a point charge Q,
  it can
• be shown that

20
Electric Potential for a Charged Spherical
Conductor

• Inside the sphere the electric potential is
  constant, but not zero.
• The field at any point outside the sphere is
  exactly the same as if the whole charge were
  concentrated at the centre of the sphere.

a
21
Zero Potential

• The practical zero potential is that of the
  Earth.
• The theoretical zero potential, according to the
  definition of V, is that of a point at infinity.

22
Potential Difference

• The potential difference across two points A and
  B is defined as the work done by the electric
  field to move a unit charge from point B to point
  A.

VBgtVA if an external agent does positive work
when moving a positive charge.

• The work done is independent of path.

23
Electric Potential between two Charged Parallel
Plates

• The work done by the electric field E to move a
  positive charge q from A to B is
• W qVAB

As W Fd and F qE
?VAB Ed
Where d is the distance between AB
24
Equipotentials

• An equipotential surface is one on which all
  points are at the same potential.
• The potential difference between any two points
  on the surface is zero.
• No work is required to move a charge along an
  equipotential.
• The surface of a conductor is an equipotential
  surface.

25
Contours
http//maxwell.ucdavis.edu/electro/potential/equi
potential.html

• The concept of potential, V, in electricity is
  equivalent to the concept of altitude, h, in the
  case of gravitational field.

26
Equipotential surfaces and Field Lines (1)
27
Equipotential surfaces and Field Lines (2)

• The equipotentials are always perpendicular to
  the field lines.
• The density of the equipotentials represents the
  strength of the electric field.
• The equipotentials never cross each other.

28
A conducting Material in an Electric Field

• Consider a pair of oppositely charged plates
  which established a uniform field between them.

29
Electrostatic Shielding

• The field inside the hollow metal box is zero.
• A conducting box used in this way is an effective
  device for shielding delicate instruments and
  electronic circuit from unwanted external
  electric field.
• The inside of a car or an airplane is relatively
  safe from lightning.

30
Comparison between Electrostatic and
Gravitational Fields
(N C-1)
(N kg-1)
WqV
WmV
31
Differences between Electrostatic field and
Gravitational field

• The gravitational force is always attractive
  while the electric force can either be attractive
  or repulsive.
• An electric field can be shielded while a
  gravitational field cannot.