ELECTRIC POTENTIAL

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 Up.

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

The potential is independent of the size of the test charge. • qo is a very small charge so it has the negligible effect on the group of charges. • Depending on the distribution of charges, the potential Vp 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 = Vb - Va = (Ua – Ub) / qo • 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 These two points a and b are near an isolated positive point charge q. rb q ds E a + + b qo ra A test charge qo moves from a to b along a radial line from a positive charge q that establishes an electric field E.

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 Vb – Va = - 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 Vb – Va = -q/40dr/r² integration limits are between ra andrb . = q/40 (1/rb – 1/ra ) 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 Va 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 = V1 + V2 + V3 + ………..+ VN

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

ELECTRIC POTENTIAL