Electric Potential•Potential Difference and Electric Potential•Potential Differences in a Uniform Electric Field•Electric Potential and Potential Energy Due to Point Charges•Obtaining the Value of the Electric Field from the Electric Potential•Electric Potential Due to Continuous Charge Distributions•Electric Potential Due to a Charged Conductor
Potential Difference and Electric Potential
• When charge is moved in the field by force, the work done by the field equal to the negative of the work done by force causing the displacement
• For small displacement ds, the work by field is
• It causes the potential energy of the field reduce by:
• For a finite displacement of the charge from a point A to a point B
Potential Difference and Electric Potential
• The potential energy per unit charge U/q0 is independent of the value of q0
• This is called the electric potential (or simply the potential) V
• The potential difference between any two points A and B
• Electric potential at an arbitrary point in an electric field equals the work required per unit charge to bring a positive test charge from infinity to that point.
• The unit: joules per coulomb or volt (v)
• Another unit:
POTENTIAL DIFFERENCES IN A UNIFORM ELECTRIC FIELD
If q0 moves from A to B, the change in potential energy is
If q0 positive, is negative, the positive charge losses its potential energy when moving in the direction of electric field.
If q0 negative , is positive, A negative charge gains electric potential energy when it moves in the direction of theelectric field
Equipotential
• The name equipotential surface is given to any surface consisting of a continuous distribution of points having the same electric potential
• A uniform electric field directed along the positive x axis. Point B is at a lower electric potential than point A. Points B and C are at the same electric potential.
ELECTRIC POTENTIAL AND POTENTIAL ENERGYDUE TO POINT CHARGES
• General expression for potential difference:
• The quantity in right hand can be expressed as
• And
• If AR
ELECTRIC POTENTIAL AND POTENTIAL ENERGYDUE TO POINT CHARGES(2)
• For a group of point charges, V at a point is
• Potential energy of two-charge system
OBTAINING THE VALUE OF THE ELECTRIC FIELDFROM THE ELECTRIC POTENTIAL
• The potential difference dV between two points a distance ds apart as
• If V(x,y,z) , then E is
Example
Example (2)
ELECTRIC POTENTIAL DUE TO CONTINUOUS CHARGE�DISTRIBUTIONS
•The electric potential dV at some point P due to the charge element dq is
•The total of V is
Example
• The electric potential at P
Example(2)
ELECTRIC POTENTIAL DUE TO CONTINUOUS CHARGE�DISTRIBUTIONS
ELECTRIC POTENTIAL DUE TO ACHARGED CONDUCTOR
• When a conductor in equilibrium, the potential difference between A and B is necessarily zero:
