Key ideas of field and electrical potential

Electric field and potential are based off on force and potential in a similar relationship as the two aren't distinct entities with the close relation, as they are simply two ways in which source charges alter the space around them

Using potential energy of charge q and source charges to define potential as

V= Uq+other sources/q

Work and potential energy defining relationship

Potential energy is defined in terms of work done by force on charge q as it moves from position i to f deltaU= -W(i->f) = - integral of si to sf (Fsds)= -integral of i to f (vector of F times vector of displacement) s=> poisiton along a line from point f to point i

Equation for force on charge q by the electric field & subbing it into the potential energy defined in terms of work & conclusion

F vector=qEfield vector q would cancel so the potential difference between two points in space is now: deltaV= Vf- Vi= -integral of si to sf (Esds)= -integral of i to f (E vector times ds vector -=> Potiential decreasing Finding potential difference between point can be found if electric field is known

Area under Es- versus- s curve between si and sf with potential difference

-, sign of decreasing potential, causes the area to be subtracted from Vi to get Vf Vf= Vi- (area......)

Finding potential from electric field

1) Draw a picture to identify point needed for finding potential and label the point as position f, sf 2) Chose zero point of potential, often at infinity, so call the point si 3) Establish coor axis from i to f along what is known or can easily determine Es component 4) Carry out integration