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. +q1 -q2 r

Coulomb’s 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

Electric Fields http://www.colorado.edu/physics/2000/applets/nforcefield.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.

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 +q

Properties of Field Lines http://surendranath.tripod.com/FieldLines/FieldLines.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.

Electric Field Patterns (1) Electric field lines for a single positive point charge Electric field lines for a single negative point charge

Electric Field Patterns (2) Electric field lines for two charges of opposite sign. Electric field lines for two equal positive charges

Electric Field Patterns (3) Electric field lines between two oppositely charged parallel plates.

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.

Electric Field Strength due to a Point Charge By Coulomb’s law E By the definition of E q r Then we have Q Notice that E depends only on Q which produces the field, and not on the value of the test charge q.

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. E1 E r1 r2 E2 -Q2 +Q1

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

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.

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. E r a

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

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.

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.

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 As and We get Hence for r 0 i.e. Electric field strength = -potential gradient

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

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. r V a

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.

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. VB>VA if an external agent does positive work when moving a positive charge. The work done is independent of path.

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 d As W = Fd and F = qE VAB = Ed Where d is the distance between AB

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.

Contours http://maxwell.ucdavis.edu/~electro/potential/equipotential.html The concept of potential, V, in electricity is equivalent to the concept of altitude, h, in the case of gravitational field.

Equipotential surfaces and Field Lines (1)

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.

A conducting Material in an Electric Field Consider a pair of oppositely charged plates which established a uniform field between them. conductor E/V m-1 x/m V/V x/m + -

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.

Comparison between Electrostatic and Gravitational Fields Electrostatic field Gravitational field Field strength (unit) Force Field strength outside isolated sphere Potential outside isolated sphere Energy transferred (N C-1) (N kg-1) W=qV W=mV

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.