The electric field intensity depends on the medium in which thecharges are placed.Electric Flux DensityThe electric flux ψ in terms of D can be defined asSuppose a vector field D independent of the medium is defined byED oε=The vector field D is called the electric flux density and is measured incoulombs per square meter.
Electric Flux DensityFor an infinite sheet the electric flux density D is given byFor a volume charge distribution the electric flux density D is givenbyIn both the above equations D is a function of charge and positiononly (independent of medium) Gauss LawIt states that the total electric flux ψ through any closed surface isequal to the total charge enclosed by that surface.encQ=ψ(i)Using Divergence Theorem(ii)Comparing the two volume integrals in (i) and (ii)This is the first Maxwell’s equation.It states that the volume charge density is the same as the divergenceof the electric flux density.Electric PotentialElectric Field intensity, E due to a charge distribution can be obtainedfrom Coulomb’s Law.or using Gauss Law when the charge distribution is symmetric.We can obtain E without involving vectors by using the electric scalarpotential V.From Coulomb’s Law the force on pointcharge Q isEQF =The work done in displacing the chargeby length dl isdlFdW .−= dlEQ .−=The negative sign indicates that the work is being done by an external agent.The total work done or the potential energy required in moving thepoint charge Q from A to B isdlEQWBA.∫−=Dividing the above equation by Q gives the potential energy per unitcharge.dlEQWBA.∫−= ABV=ABV is known as the potential difference between points A and B.1. If is negative, there is loss in potential energy in moving Qfrom A to B (work is being done by the field), if is positive, thereis a gain in potential energy in the movement (an external agent doesthe work).ABVABV2. It is independent of the path taken. It is measured in Joules perCoulomb referred as Volt.The potential at any point due to a point charge Q located at the origin isThe potential at any point is the potential difference between thatpoint and a chosen point at which the potential is zero.Assuming zero potential at infinity, the potential at a distance r fromthe point charge is the work done per unit charge by an external agentin transferring a test charge from infinity to that point.ldEVr.∫∞−=If the point charge Q is not at origin but at a point whose positionvector is , the potential at becomesr r)( rV||4)(rrQrVo −=πεrQVoπε4=
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