Electric Fields and Capacitors

The basis of Electric storage

• Two objects are just resolved when the central diffraction maximum of one object is at the first minimum of the other. (Rayleigh’s criterion)

As before, is approximately tan = y/L Circular aperture has diameter d

A Learning Summary

ddR

22.122.1

sin 1

What type of forces could act on e-?

Gravity, if . . .• another mass is around.

Electricity, if . . .• another charged object is around.

Magnetism, if . . .• the e- is in a magnetic field

The weak nuclear force, if . . .• any other fermion is around

Gravity’s force between e- and p+

Force between two objects due to gravity:

m1 = me = 9.11 E-31 kgm2 = mproton = 1.67 E-27 kgr = 1 nm = 10-9 mF = 1.01 E-49 N

221

r

mmGF

Electrical force between e- and p+

Force between two objects due to Coulomb (electric) attraction:

q1 = qe = 1.602 E-19 Cq2 = qproton = 1.602 E-19 Cr = 1 nm = 10-9 mF = 2.31 E-10 N

221

r

qqkF

Nuclear force between e- and p+

Force between two objects due to the weak nuclear force:

s = 2mc2E = 1 GeV2 = 2.5 E-20 J2

mW = 1.42 E-25 kgr = 1 nm = 10-9 mGF = 4.52 E 14 J-2

F < 1 E -100,000 N

hcrmF

WseGF 2/

Comparing forces between e- and p+

Electric: F= 2.31 E-10 NGravity: F= 1.01 E-49 NNuclear: F < 1 E -100,000 NIf I had 1% more electrons than protons, and

I stood an arm’s length away from a similarly imbalanced person, the force between us would be great enough to lift a weight the size of . . .

• The earth!

How can a force act at a distance?

If I took my electron away from the proton and brought a positron (positive e) near the proton, the positron would . . .

• accelerate away from the protonSo, does my proton exert a force if no one is

around to feel it?• Force, no. But we can define an electric

field which describes the force a charge would feel if it came near the proton

How can a force act at a distance?

A charge creates an electric field that fills space, whether or not any other charge is around to feel its effects!

Make Predictions for the Activity, then Answer Questions 1-7 of the Activity

What’s a Field?

Electric field E = F/q, where q is the charge feeling the force

Since forces obey the law of linear superposition (i.e., they add), electric fields add too!

What does a “field” look like?

Finish the Activity, working as far as you can in the time allowed

Charges in Conductors Electric fields are created when positive charges

and negative charges are separated A uniform electric field existing over a region sets

up a potential difference between points in that region: V=Ex, where x is the distance along a field line.

If I apply a potential difference across a conducting object (including semi-conductors), charges experience a force, and charge carriers will flow until the potential difference is removed.

What if charge can’t flow? Consider charge separated by two metal

plates– A potential difference exists between the plates– An electric field exists between the plates,

pointing from positive plate to negative plate– No current can flow

Introducing, . . . The Capacitor

Introducing, . . . Capacitance

The battery provides the work needed to move the charges and increase their potential energy

What determines capacitance?

C = 0 A/d

More about capacitors

More about capacitorsU = Vq = Ve

1 eV = 1.602 x 10-19 J

= energy to move electron through 1 volt