Charge Comes in + and – Is quantized elementary charge, e, is charge on 1 electron or 1 proton e =  Coulombs Is conserved total charge remains constant

Coulomb’s Law F = kq 1 q 2 /r 2 k = 8.99  10 9 N m 2 / C 2 q 1, q 2 are charges (C) r 2 is distance between the charges (m) F is force (N) Applies directly to spherically symmetric charges

Spherical Electric Fields F =kqq 0 r 2 E = F = kq q 0 r 2

Why use fields?  Forces exist only when two or more particles are present.  Fields exist even if no force is present.  The field of one particle only can be calculated.

Field around + charge Positive charges accelerate in direction of lines of force Negative charges accelerate in opposite direction

Field around - charge Positive charges follow lines of force Negative charges go in opposite direction

For any electric field  F = Eq  F: Force in N  E: Field in N/C  q: Charge in C

Principle of Superposition When more than one charge contributes to the electric field, the resultant electric field is the vector sum of the electric fields produced by the various charges.

Field around dipole

Caution… Electric field lines are NOT VECTORS, but may be used to derive the direction of electric field vectors at given points. The resulting vector gives the direction of the electric force on a positive charge placed in the field.

Field Vectors

Electric Potential U = kqq 0 r V = U = kq q 0 r (for spherically symmetric charges)

Electrical Potential  V = -Ed  V: change in electrical potential (V) E: Constant electric field strength (N/m or V/m) d: distance moved (m)

Electrical Potential Energy  U = q  V  U: change in electrical potential energy (J) q: charge moved (C)  V: potential difference (V)

Electrical Potential and Potential Energy Are scalars!

Potential Difference  Positive charges like to DECREASE their potential.  (  V < 0)  Negative charges like to INCREASE their potential.  (  V > 0)

Announcements 10/4/2015  Lunch Bunch Wednesday  Graded quiz tomorrow  Exam Friday

Potential surfaces positive negative high highest medium low lowest

Equipotential surfaces high low

Today...  More with electric potential and potential energy.

Definition: Capacitor  Consists of two “plates” in close proximity.  When “charged”, there is a voltage across the plates, and they bear equal and opposite charges.  Stores electrical energy.

Capacitance C = q /  V C: capacitance in Farads (F) q: charge (on positive plate) in Coulombs (C) V: potential difference between plates in Volts (V)

Energy in a Capacitor U E = ½ C (  V) 2 U: electrical potential energy (J) C: capacitance in (F) V: potential difference between plates (V)

Capacitance of parallel plate capacitor C =  e  0 A/d C: capacitance (F)  e : dielectric constant of filling  0 : permittivity (8.85 x F/m) A: plate area (m 2 ) d: distance between plates(m)

dielectric Parallel Plate Capacitor E +Q -Q V1V1 V2V2 V3V3 V4V4 V5V5

Cylindrical Capacitor - Q + Q E

Problem #2 Calculate the force on the 4.0  C charge due to the other two charges. 60 o +4  C +1  C

Problem #3 Calculate the mass of ball B, which is suspended in midair. A B q = 1.50 nC q = nC R = 1.3 m

Problem #2 Two 5.0  C positive point charges are 1.0 m apart. What is the magnitude and direction of the electric field at a point halfway between them?

Problem #4 Calculate the magnitude of the charge on each ball, presuming they are equally charged. AB 0.10 kg 1.0 m 40 o 1.0 m 0.10 kg