Gauss's Law for Electric Fields Flashcards
The Fundamental Forces
- gravitational forces
- electromagnetic forces
- strong nuclear force
- weak nuclear force
Field
- interaction at a distance
- certain objects set up a field around them which other particles interact with
- they are illustrated with arrows and field lines
Fields and Flow
-nothing is flowing in a magnetic or electric field, but the mathematical relationships between various quantities in these fields will be the same as in fluid flow
Electrostatics and Magnetostatics
- stationary charges have constant electric fields; electrostatics
- steady currents have constant magnetic fields; magnetostatics
Steady Currents
- a steady current I, means a continuous flow that has been going on forever without charge piling up anywhere
- a moving point charge cannot constitute a steady current since it is here one instant and gone the next
Coulomb’s Law
Electric Field of a Point Charge
|E(|r) = kq/r²r^
k = 1/4πε0 = 8.99x10^9 Nm²/C²
Electromagnetism - Superposition Principle
-the net response at a given place is the sum of the responses which would have been caused by each stimulus individually
Continuous Charge Distribution
Charge Density
ρ = Q/V dq = ρdV
Continuous Charge Distribution
Electric FIeld
|E(|r) = ∫ kdq/r² r^ = ∫ kρ/r² r^ dV
The electric field is the integral over all charge of kdq/r² or the integral over the entire volume of kρ/r².
Gauss’s Law for Electric Fields - Integral Form
∮(|E . n^)dA = Q/ε0
The integral of electric field in the direction perpendicular to the surface across a closed surface is equal to the total charge enclosed by that surface divided by the permitivity of free space
OR
An electric charge produced an electric field and the flux of that field passing through any closed surface is proportional to the total charge contained within that surface.
Solid Angle
ΔA’ = r² x ΔΩ
where A’ is the are on the surface of the sphere
r is the radius of the sphere and Ω is the solid angle
- to go right around a sphere or any closed surface you have to travel around by Ω=4π steradians
- this is why the surface area of a sphere is 4πr²
Gauss’s Law for Electric Fields - Integral Form
Multiple Point Charges
∮(|E . n^)dA = ∮ Σ|E.n^ dA = ∮|E1.n^dA + ∮|E2.n^dA + …
=q1/ε0 + q2/ε0 + …
=Q/ε0
Gauss’s Law for Electric Fields - Integral Form
Charge Outside of the Closed Surface
-the net flux from any charge outside of the closed surface is zero as the flux into the surface from that charge is equal to the flux out, so net flux is zero.
Gauss’s Law for Electric Fields
Sources and Sinks
-net flux will tell you whether inside a closed surface you have a net source or sink of electric field lines and whether the net flow is out or in
Is a positive charge a source or a sink?
-positive charge acts as a source of field lines like a tap within the enclosed volume generating the flow out of the surface containing that volume