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Electrostatic:Gauss’ Law

Chapter 23 Halliday-Resnick 9th Ed.

Monday, 2 February 2012

Relates the electric fields at points an a closedGaussian surface to the net charge enclosed by thesurface Φ =∙ =

Gauss’ Law:

0. Draw the diagram1. Select a closed surface2. Solve ∮ ∙3. Solve ∮ ∙ =

Spherical Symmetry

= 1Spherical shell

at ≥= 0 at <

= 1at ≥

=43 = 43== at <

Spherically symmetric charge distribution

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Electrostatic:Electric Potential

Chapter 24 Halliday-Resnick 9th Ed.

Thursday, 6 February 2012

Physics: identify basic forces in our world to determine whether a force is conservative can a potential energy be associated with it?physicists and engineers discovered that the electricforce is conservative It has an associated electric potential energy

Electric potential energy: An Electric force act between two or more particles Assign an Electric Potential Energy to the system

initial ( ) final ( )Change of states

Δ = − = −Conservative force → path independent

Reference: = infinite separation → = 0 = neighboring particles → = = ΔU = −

Work done bythe force duringmove from ∞

In the figure, a proton moves from point topoint in a uniform electric field directed asshown.(a) Does the electric field do positive or

negative work on the proton?(b) Does the electric potential energy of the

proton increase or decrease?

Electrons are continually being knockedout of air molecules in the atmosphere bycosmic-ray particles coming in from space.Once released, each electron experiences anelectrostatic force P due to the electric fieldIf that is produced in the atmosphere bycharged particles already on Earth. NearEarth's surface the electric field has themagnitude E = 150 N/C and is directeddownward. What is the change Δ in theelectric potential energy of a releasedelectron when the electrostatic force causesit to move vertically upward through adistance d = 520 m (Fig. 24-1)

= ∙ = ∙ = cos= 1.2 × 10 JΔ = − = −1.2 × 10 J<

= [J/C] (scalar)Δ = − = − = −= 0== − [volt (V)]

Electric Potential:

1eV : the amount of energy to moveelementary charged particle

(electron/proton) inside a potential of 1V1.60 × 10 C 1 J/C = 1.60 × 10 J

Work done bythe force duringmove from ∞

In the figure of Checkpoint 1, we move theproton from point to point in a uniformelectric field directed as shown.(a) Does our force do positive or negative work?(b) Does the proton move to a point of higher orlower potential?

Equi-potential

surface

Calculating from

= ∙ = ∙= ∙− = − ∙= 0== − ∙

− =?

Potential due to a Point ChargeMove from to infinity∙ = cos− = − ∫ ∙; = 0; = = 1

0 − = − 1= 1 = − 1

= 1 + → +− → −

What is the electric potential at pointP, located at the center of the squareof point charges shown in Fig. 24-8a?The distance d is 1.3 m, and thecharges are ql = +12 nC, q2 = -24 nC,

q3 = +31 nC,q4 = +17 nC.

In Fig. 24-9a, 12 electrons (ofcharge -e) are equally spacedand fixed around a circle ofradius R. Relative to V = 0 atinfinity, what are the electricpotential and electric field atthe center C of the circle dueto these electrons?

If the electrons are movedalong the circle until they arenonuniformly spaced over a120° arc (Fig. 24-9b), whatthen is the potential at C?How does the electric field atC change (if at all)?

Potential Due to an Electric Dipole

= = + = 1 += ( ) − ( )( ) ( )≫( ) − ≈ cos( ) ( ) ≈= cos= 1 cos