Charge Comes in + and – Is quantized Is conserved elementary charge, e, is charge on 1 electron or 1 proton e = 1.602 10-19 Coulombs Is conserved total charge remains constant
Milikan’s Experiment By adjusting the voltage, a drop could be suspended. Then FG = FE Knowing density of oil, FG & total charge could be determined. Finding lowest common denominator led to elementary charge.
Coulomb’s Law F = kq1q2/r2 k = 8.99 109 N m2 / C2 q1, q2 are charges (C) r2 is distance between the charges (m) F is force (N) between charges Applies directly to spherically symmetric charges
Electric Forces Mimic Gravitational Forces Formulas are similar in structure Both diminish exponentially with distance Add vectors to determine total force on a charge Difference: Electrical forces can be attractive or repulsive Opposite electrical charges attract
Spherical Electric Fields F =kqq0 r2 force E = F = kq q0 r2 field
Why use fields? Forces exist only when two or more particles are present. Fields exist even if no force is present. (Think gravity again!) The field of one particle only at a time can be calculated. Multiple particles create vector sums that yields resultant field
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 E = F/q F: Electric Force in N E: Electric 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 = kqq0 r V = U = kq q0 r potential energy V = U = kq q0 r potential (for spherically symmetric charges)
V = -Ed Electrical Potential V: change in electrical potential (V) E: Constant electric field strength (N/m or V/m) d: distance moved (m)
Electrical Potential Energy U = qV U: change in electrical potential energy (J) q: charge moved (C) V: potential difference (V)
Electrical Potential and Potential Energy Are scalars! (no direction)
Potential surfaces high highest medium low lowest positive negative
Equipotential surfaces high low
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 / DV C: capacitance in Farads (F) q: charge (on positive plate) in Coulombs (C) V: potential difference between plates in Volts (V)
UE = ½ C (DV)2 V: potential difference between plates (V) Energy in a Capacitor UE = ½ C (DV)2 U: electrical potential energy (J) C: capacitance in (F) V: potential difference between plates (V)
Capacitance of parallel plate capacitor C = 0A/d C: capacitance (F) 0 : permittivity (8.85 x 10-12 F/m) A: plate area (m2) d: distance between plates(m)
Capacitors in Circuits +Q -Q +Q -Q
Equivalent Capacitance series Charge is same on all capacitors in series arrangement. 1/Ceq = 1/C1+ 1/C2 + 1/C3
Equivalent Capacitance parallel Voltage is same on all capacitors in parallel arrangement. Ceq = C1+ C2 + C3
Parallel Plate Capacitor +Q -Q V1 V2 V3 V4 V5 dielectric E
Cylindrical Capacitor - Q + Q E
Calculate the force on the 4.0 C charge due to the other two charges. Problem #2 Calculate the force on the 4.0 C charge due to the other two charges. +4 C 60o 60o +1 C +1 C
Calculate the mass of ball B, which is suspended in midair. Problem #3 Calculate the mass of ball B, which is suspended in midair. q = 1.50 nC A R = 1.3 m q = -0.50 nC B
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. 40o 1.0 m 1.0 m A B 0.10 kg 0.10 kg