Week 3 Flashcards
Obtain Gauss’s law in diff form
Gaussian surfaces have
Electric fields are constant (thereby simplifying Flux integrals)
When to use Gaussian surfaces? when not?
When there is spherical, cylindrical or planar symmetry
In absence of these symmetries use a superposition of electrical fields which feature combinations of spherical, cylindrical and planar charge distributions
Deduce M2 (electrostatic)
Using formula for curl of a product of a scalar function and a vector
Derive electric potential
And because curl of E = curl of (neg grad of φ)
Define electric potential for charged density
Implies (intuition) ?
Electric field at any point gives a vector which points in the direction of fastest decrease in the potential φ
Equipotent surface
Surface upon which potential is constant
Electric field lines are perpendicular to equipotent surfaces
The potential is measured in
Volts which is equivalent to Newton-metres per coulomb
Derive work per unit charge
F act on test charge Q
Therefore force needed to act on Q to balance F is -F
Potential energy of static system of discrete charge
Given W1 = 0
Femtosecond
10**-15 seconds
Electric field in a conductor
= 0
When placed in an external electric field the free charges move subject to external field.
For a metal, electrons move in opposite direction to field lines until they reach surface of conductor.
These electrons leave behind positively charged atoms causing an induced charge in the opposite direction to field. This induced field grows until it balances the external field and equilibrium is reached.
Q in a conductor
= 0
By gauss’s law as E(r) = 0
Show that the potential inside a conductor is constant
Where rs is a radial vector on the surface of the conductor
Second integral is equal to zero
(Take it for granted)
motivate a faraday cage
Given a cavity within a conductor
Given a closed path P passing through the conductor and the cavity
Electric field of a single point charge q located at the origin
