ELECTRIC POTENTIAL SLIDES BY ZIL E HUMA

ELECTRIC POTENTIAL The force between two charges depends on the magnitude and sign of each charge. DEF: The potential energy per unit test charge is known as the electric potential.

Let we have a collection of charges. We have to determine the electric potential of these charges at a point P. We place a +ve test charge at the infinite distance from the collection of charges, where the electric potential will be zero. We then move this test charge from infinity to the point P, and in this process the potential energy changes from 0 (zero) to U p.

The electric potential V p at P due to the collection of charges is then defined as V p = U p /q o where the q o is the test charge. Electric potential is a scalar quantity because Up and q o both are the scalar quantities.

The potential is independent of the size of the test charge. q o is a very small charge so it has the negligible effect on the group of charges. Depending on the distribution of charges, the potential V p may be +ve, -ve or zero. According to the above equation the potential energy is positive. If we move the positive test charge from infinity to that point, the electric field do negative work, which indicates that the test charge has experienced a repulsive force.

ELECTRIC POTENTIAL BETWEEN TWO POINTS a AND b. We move a test charge qo from a to b. The electric potential difference is defined by  V = V b - V a = (U a – U b ) / q o The potential at b may be greater than, less than, or the same as the potential at a,depending on the difference between the two points.

UNIT OF THE ELECTRIC POTENTIAL The SI unit of potential that follow the above equation is the joule / coulomb which is equal to the volt (abbreviated V). 1 volt = 1 joule / coulomb

So we have  U = q  V When any charge q moves between two points whose potential difference is  V, the system experiences a change in potential energy  U. When  V is expressed in volts and q in coulombs,  U comes out in joules.

ELECTRON VOLT Electron volt is the unit of energy. If we express  V in volts and q in units of the elementary charge e, then  U is expressed electron volt (eV).

POTENTIAL DUE TO A POINT CHARGE ++ a q b rbrb rara ds qo E A test charge qo moves from a to b along a radial line from a positive charge q that establishes an electric field E. These two points a and b are near an isolated positive point charge q.

A positive charge qo moves from point a to b along a radial line. From figure we can see that both E and ds has the radial component i.e.,dr So ds = dr E.dr =E dr We know already that V b – V a = -  E.ds = -  E.dr = -  E dr Using the expression for the electric field of a point charge, E = q/4   0 r²

So we have V b – V a = - q/4   0  dr/r² integration limits are between r a and r b. = q/4   0 ( 1/ r b – 1/ r a ) This equation gives the potential difference between the points a and b..

If we wish to find the potential difference at any point, then we choose a reference point at infinity. We choose a to be at infinity and define V a to be zero at this position. Making these substitutions and dropping the subscript b we get V = 1/4   0 ( q / r ) This equation is also valid for any spherically symmetric distribution of total charge q,as long as r is greater than the radius of the distribution.

POTENTIAL DUE TO A COLLECTION OF POINT CHARGES The potential at any point due to a group of N charges is found by 1.Calculating the potential Vi due to each charge, as if the other charges were not present, and 2. Adding the quantities so obtained. V = V 1 + V 2 + V 3 + ………..+ V N

So we have i=N V =  V i = 1/4   0  q i /r i i=1 i where q i is the value (magnitude and sign) of the ith charge. And r i is the distance of the ith charge from the point in question.