Electric Potential (III) - Fields Potential Conductors

Potential and Continuous Charge Distributions We can use two completely different methods: Or, Find from Gauss’s Law, then…

Ex 1: Given V=3x2+12x-1, find where E=0.

Ex 2: The Electric Potential of a Dipole y a a x -q +q P Find: a) Potential V at point P. b) What if x>>a ? c) Find E.

Solution

Ex 3: Find the potential of a finite line charge at P, AND the y-component of the electric field at P. P r d dq x L

Solution

Ex 3: Find the potential of a uniformly charged sphere of radius R, inside and out. R

Uniformly Charged Sphere,radius R V r R

Recall that the electric field inside a solid conducting sphere with charge Q on its surface is zero. Outside the sphere the field is the same as the field of a point charge Q (at the center of the sphere). The point charge is the same as the total charge on the sphere. Find the potential inside and outside the sphere. +Q R

Solution Inside (r<R), E=0, integral of zero = constant, so V=const Outside (r>R), E is that of a point charge, integral gives V=kQ/r

Solid Conducting Sphere,radius R V r R

Quiz A charge +Q is placed on a spherical conducting shell. What is the potential (relative to infinity) at the centre? +Q keQ/R1 keQ/R2 keQ/ (R1 - R2) zero R1 R2

Calculating V from Sources: Point source: (note: V0 as r ) or ii) Several point sources: (Scalar) iii) Continuous distribution: OR … I. Find from Gauss’s Law (if possible) II. Integrate, (a “line integral”)