Potential, V, at every point with multiple charges

With multiple charges (q1, q2), the electrical potential at a point in space is the sum of all the potentials due to each charge as depicted by V= sumi x 1/4pieeo x qi/ri

Symbol of distance meaning

ri is the distance from the charge q to the point where the potential is being calculated as potential obeys the laws of superposition, like the electric field

Contour and elevation graphs representation in terms of the potential of the dipoles

Sum of the positive and negative charges with leading to numerous applications as the result with the measurement of the equipotential lines in comparison to fields

Main characteristic of finding potential with multiple charges

Potential is a scalar, so the net potential is the addition of the charges, q, and ri, distance from charge to the point where the potential is calculated, so no need for components or angles like potential energy

Basis for determining potential of a continuous charge distribution in a rod or sphere

Vsphere= 1/4pieeo x Q/r as r>_R (potential of the surface) Vo= V(r=R)= Q/4pieeoR Q= 4pieeoRVo V= R/r x Vo

Assumptions with potential of a continuous charge distribution of a rod or charged sphere

Easier; not a vector, but scalar; uniformly charged, as charges are evenly spaced over object

Steps involving the solving for potential of a continuous distribution of charges

1) Model distribution as a simple shape 2) Visualize a pictorial representation - Draw pic, establish coor system. and identify P needed to be calculated for electrical potential - Divide total charge Q into small pieces of charge using shapes where the determination of knowing V is known as it is often, but not always, with point charges - Identify distances 3) Solve with V= sum of Vi - Use superposition for an algebraic expression for potential at P with coordinates remaining as variables - Replace small charge with equivalent expression involving charge density and a coordinate such as dx as it is a critical step to go from the transition od sum to an integral as the coordinate value need to serve as the integral variable -All distance are coordinates - Sum becomes an integral and the integration limits are based up the coor system