Understanding Coulomb's Law and Electrostatic Fields
Explore Coulomb's Law, Poisson's Equations, Laplace's Equations, Scalar Potentials, Point Charges, and more in the field of electrostatics. Learn about the relationship between electric fields, potentials, charge distributions, and the principles governing electrostatic interactions.
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Presentation Transcript
Coulombs Law Section 36
Electrostatic field Poisson s equation
In vacuum, = 0. Then Poisson s equation becomes Laplace s equation
Theorem: Scalar potential cannot have an extremum in vacuum. Proof: Suppose has an extreme value somewhere Then 0 at that point All have the same sign AND But that violates
Point charge. Field is spherically symmetric. No or dependence. E is oriented along a radius vector from the point charge. E = E(R) is a function only of the distance R from the charge. Coulomb s law Inversely proportional to the square of the distance from the charge.
System of charges Superposition principle: E-field at a field point is the vector sum of the fields form all charges Potential at field point is sum of potentials from all charges
Continuous charge distribution Field point = charge density
Point charge Poisson s equation
