Electric Potential Assignment Help

Electromagnetism - Electric Potential

Electric Potential

The amount of work done to bring a unit positive charge from infinity to that point against the electric field of a given charge without charging

Kinetic energy: V = ∫r ∞ - E dx = Q/4πε0r it is a scalar quantity and its unit is volt. 

1 volt = 1j/1C

The dimensions are MI LT3 A-1

Potential difference 

?V = v2 - v1 = ∫r2 r1 - E dr

= Q / 4πε0r|r2r1 = Q / 4?ε0 [ 1/r2 - 1/r1

Equipotential surface is the surface, where the potential is equal at every point. For a point charge, a sphere will be equipotential surface with charge at the centre of the sphere. Equipotential surface for a long line charge is cylinder within charge along axial line, for a dipole, equipotential surface is a plane passing through equatorial line. 

The work done in carrying a charge form one pint to another in a equipotential surface is zero. 

The electric lines of force are always perpendicular to the equipotential surface.

Every conductor is an equipotential surface as electric filed E is perpendicular to it. 

Electric field along the equipotential surface is zero these surfaces do not intersect each other. 

E = - ?V

Electric field and surface charge density are maximum at pointed ends.

Electric field intensity due to a shell

inside = 0                                     x < R

surface = Q/4πε0R                 x = R

outside = Q/4πε0x                  x > R

Electric potential due to a shell

inside = Q / 4πε0R = V surface            x < R

surface =Q / 4πε0R                                x = R

outside   = Q / 4πε0x                              x > R

Electric filed intensity due to a dies of radius r having surface charge density σ at a point p, distant x on the axial line is

E = σ/2ε0 [ 1 - x / x2 + r2]    = σ / 2ε0 if r ---> ∞

Or x --> 0, that is at the centre of the disc

Electric potential V = (σ/2ε0) [x2 + r2   - x] 

Dipole, moment p = q (2I) the direction is along negative to positive side.

Electric filed intensity due to a dipole
Along axial line

Eaxial = 2px / 2ε0 (x2 - I2 )

For a short dipole x >>I E axial = 2p / 4πε0x3

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