Physics - Revision Notes on Electric Fields

Electric field is a region in space where a stationary charge experiences a force

The direction of an electric field is defined as the direction in which a positive charge would move if it were free to do so

The electric field strength E, is defined as the force per unit charge acting on a small positive charge placed at that point,

 i.e.     E = F/Q  N C^-1

The force between charges according to coulomb is

proportional to the product of the charges and inversely proportional to the square of the distance between them

 i.e F = kQ₁Q₂/r²

  where k is a constant of proportionality, the value of which depends on the medium around the charges

•             this law applies to point charges but can be used for charged spheres provided their radii are small compared to their separation

The potential difference V_AB between two points A and B in an electric field is the work done W, in moving a unit positive charge from B of lower potential to A of higher potential against the direction of the line of action of the force on the unit charge.

That is V_AB = W/Q   i.e.  W = VQ   SI unit of V is Volts

But also, work done (which is energy)

W = Fd, therefore Fd = VQ with units of V C

·           Rearranging, F/Q = V/d,

·           but F/Q is the force per unit charge which is the definition of electric field strength E.

·           Hence for a uniform field, the field strength E = V/d V m^-1

·           E has 2 equivalent SI units, V m^-1 = N C^-1

From Coulomb’s Law, the force on a test charge Q₁, a distance r from the isolated point charge Q₂ is given by,

F = kQ₁Q₂/r²

The electric field E at the location of the test charge q, is given by

 E = F/q

Therefore the electric field due to the isolated point charge is

 F = kQ₁Q₂/r²

Electric field has been defined as the force per unit charge

Electric potential V, at a point in an electric field is defined as the work done or potential energy PE, in bringing unit positive charge from infinity to the point

 i.e V = PE/Q

The field strength is equal to the negative of the potential gradient at that point

V = PE/Q = (F x r)/q = (kQ1Q2/r2x r)/q   = kQ/r 

            where k = 1/4πε0r

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