Storage by Electrons: Electric Fields and Capacitors But first, a discussion of the exam

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: m 1 = m e = 9.11 E-31 kg m 2 = m proton = 1.67 E-27 kg r = 1 nm = m = 1 E-9 m F = 1.01 E-49 N

Electrical force between e- and p+ Force between two objects due to Coulomb (electric) attraction: q 1 = q e = E-19 C q 2 = q proton = E-19 C r = 1 nm = m F = 2.31 E-10 N

Comparing forces between e- and p+ Electric: F= 2 E-10 N Gravity: F= 1 E-49 N Nuclear:F < 1 E -100,000 N A 1kg mass needs ~10N of force to prevent it from falling on the surface of the earth so electric force seems small. However, ~1E23 electrons per cubic centimeter.  enormous forces possible from electric charges

Coulomb’s Law

Forces on Charges Unlike charges attract. Like charges repel.

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 proton So, 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

The Electric Field When E is known, the force, F, on a charge, q 0, is given by: F = q 0 E The direction of E is the direction of the force on a positive charge.

The Electric Field For a point charge q, the force on q 0 is, Then, at q 0 ’s location,

Electric Field of a Positive Point Charge The picture shows the electric field vector at several points.

Electric Field Lines Electric field lines show the direction of E at any point. The magnitude of E is proportional to the density of electric field lines. Electric field lines originate on positive charges and terminate on negative charges, unless they extend to infinity.

Electric Field Lines for a Negative Point Charge

Consider Two Point Charges The two fields point toward the negative charges that produce them, and must be added as vectors to get the final result.

Addition of Electric Field (continued) The horizontal components of the two vectors add to zero, so the resultant points downward. Its magnitude is equal to the sum of the vertical components of the two vectors. Since it is an equilateral triangle, each vector makes an angle of 30° with the vertical direction. Then: E 1vertical = E 1 cos 30° and E = 2 E 1 cos 30°

Addition of Electric Field (continued) The answer is: E = 2(1.0 × 10 5 N/C) cos 30° E = 1.7 × 10 5 N/C Downward

What do you think? What do you think the field from a positive point charge will look like? How will the field change if the charge is negative? How will the field lines change if the magnitude of the charge is increased? What do you think the field lines for a pair of oppositely charged point charges (one positive, one negative) look like?

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

Class 10 Activity Start Activity 10 on WebCT Tools. Wait for class before completing parallel plate part of the activity.

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=E  x, where  x is the distance along a field line.  If I apply a potential difference across a conducting object (including semiconductors), 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,... Capacitance The battery provides the work needed to move the charges and increase their potential energy

Before the next class,... Start Homework 12 (Due Monday, Feb. 25) Do Activity 10 Evaluation by Midnight tonight Do the Readings for Class 10 (if you have not completed already) Do Reading Quiz