Physics Exam 1 Electromagnetism Summary Outline

Important Numbers One Electron Charge e = 1.602 x 10^-19 C Electrostatic Constant k = 8.99 x 10^9 Nm^2/C^2 Avogadro # 1 mole = 6.02 x 10^23 atoms Gravitational Constant G = 6.67430 x 10^-11 Conversion atm <-> C 1 atm = 1.013 x 10^5 Pa 1C = 10^-6 uC = 10^-9 nC Important Equations Coulombs Law Fe = k q1q2 / r^2(12) For Two Point Charges: Fe = Electric Force k = Coulomb's Constant q1, q2 = charge on objects r = distance between objects Electric Force due to an electric field F = QE F = electric force Q = (Test Charge) E = Electric Field E = F/Q Electric Field at Point P E(p) = Sum (kQ / R^2) R-hat R = distance from P to charge Q Q = Charge creating field R-hat = Unit vector from P to Q Superposition of electric charges F = kQ Sum (qi / ri^2) (ri-hat) Sum is over individual point charges For Continuous Charge lambda = Q/L sigma = Q/A X/Y sqrt(3) sqrt(3) (units in equation) 2m 60 degrees Chapter 2 Stuff F = k q1 q2 / r^2 E1 = 3.854 x 10^-22 E = k Q/R^2 E = F/Q E = lambda / (2 pi epsilon_0 R) (Line) Area of sphere = 4 pi R^2 Area of cylinder = 2 pi r L epsilon_0 = 8.85 x 10^-12 Integral E.dA = Q_enc / epsilon_0 (Gauss' Law) Flux = EA Cos theta Work = FD Work = 1/2 mv^2 Potential Difference V = U/q U = PE V = Integral E . ds Exponent Rules Product: a^x a^y a^z = a^(x+y+z) Quotient: a^x / a^y = a^(x-y) Power: (a^x)^y = a^(xy) Power of Product: (ab)^x = a^x b^x Power of a Fraction Rule: (a/b)^x = a^x / b^x Zero Exponent: a^0 = 1 Negative Exponent: a^-x = 1/a^x Fractional Exponent: a^(x/y) = y-th_root(a^x) Important Numbers One Electron Charge e = 1.602 x 10^-19 C Electrostatic Constant k = 8.99 x 10^9 Nm^2/C^2 Avogadro # 1 mole = 6.02 x 10^23 atoms Gravitational Constant G = 6.67430 x 10^-11 Conversion atm <-> C 1 atm = 1.013 x 10^5 Pa 1C = 10^-6 uC = 10^-9 nC Important Equations Coulombs Law Fe = k q1q2 / r^2(12) For Two Point Charges: Fe = Electric Force k = Coulomb's Constant q1, q2 = charge on objects r = distance between objects Electric Force due to an electric field F = QE F = electric force Q = (Test Charge) E = Electric Field E = F/Q Electric Field at Point P E(p) = Sum (kQ / R^2) R-hat R = distance from P to charge Q Q = Charge creating field R-hat = Unit vector from P to Q Superposition of electric charges F = kQ Sum (qi / ri^2) (ri-hat) Sum is over individual point charges For Continuous Charge lambda = Q/L sigma = Q/A X/Y sqrt(3) sqrt(3) (units in equation) 2m 60 degrees Exponent Rules Product: a^x a^y a^z = a^(x+y+z) Quotient: a^x / a^y = a^(x-y) Power: (a^x)^y = a^(xy) Power of Product: (ab)^x = a^x b^x Power of a Fraction Rule: (a/b)^x = a^x / b^x Zero Exponent: a^0 = 1 Negative Exponent: a^-x = 1/a^x Fractional Exponent: a^(x/y) = y-th_root(a^x) Important Terms/Concepts Polarization Description of how charge is redistributed Open Dipole Conductor Perfectly Insulated: - + Separation of charges Neutral (no net charge) No current flows Can still experience force and torque from external field Insulator Charges are fixed Can't move Coulomb's Law Gives the magnitude of the force between two point charges If charges are opposite, force is attractive If charges are same, force is repulsive What happens to the mag of E-field? Electric Field strength is a measure of the amount of force exerted on a test charge The magnitude of the electric field from a point charge depends on the distance from the charge and the magnitude of the charge. How to find net charge from atoms Find mass Mass -> moles Moles -> # of atoms of atoms -> # of electrons of electrons * charge on 1 electron = total charge Sum F = (k q1 q2 / r^2) (i + j + k) Net Charge = ... Practice Problems Electric Field What is E at (0,0)? F = qE V = kQ/r Continuous Charge Distributions Continuous Charge Distributions E = Integral dE lambda = Q/L sigma = Q/A rho = Q/V When the object is very long/far from E E = lambda / (2 pi epsilon_0 r) Other Charges Sum the components of E-field Point Charge What is E-field at point P? Exploration Work Charge Density lambda (Wire/Rod) = Q/L sigma (Plane) = Q/A rho (Volume) = Q/V Line: E = Q / (2 pi epsilon_0 R) E = lambda / (2 pi epsilon_0 R) Units: C/m Area: E = sigma / (2 epsilon_0) Units: C/m^2 Volume: E = (rho R) / (3 epsilon_0) Units: C/m^3 One with uniform E-field is sigma / epsilon_0 Area = 4 pi r^2