Physics Cheatsheet Electricity and Magnetism, Cheat Sheet of Physics

Download Physics Cheatsheet Electricity and Magnetism and more Cheat Sheet Physics in PDF only on Docsity! SLAC Lab Physics Handout Electricity & Magnetism ELECTRICITY The unit of charge is the Coulomb, C. Induced Charge: in an object, positive and negative charges have been separated due to presence of nearby charge. Coulomb’s Law: =. = P= ale! = plan m? CF where k = 8.99 x 10° For 3+ charges the net force on one charge is calculated by the Principle of Superposition. The method is as follows: Principle of Superposition states that the net force is the sum of the individual forces, Fret = F + P+ wet Fa, for n charges. 1) Determine direction of force by signs of charges. 2) Then evaluate force disregarding direction (only consider magni- tudes). 3) Finally include direction in final Vector answer. The Elementary Charge: electric charge is quantized, con- served and is a constant of nature, e + 1.602 x 10~19C. Field due to a Point Charge: B=k4. Again, the Principle of Superposition allows us to calculate the net electric field at a point for 2+ charges: Ene = E+ Bot... + En, forn charges. Field Due to an Electric Dipole: B= 4%, where p = qd. Ines i is a r Electric Field Due to a Continuous Charge Distribution: There are four different types of distributions: Name Symbol SI Unit Charge q Cc Linear Charge Density BN & Surface Charge Density o & : c ‘Volume Charge Density p a Force on a Point Charge in an External Electric Field: B=qk. F has the same direction as E if qis positive and the opposite direction if q is negative (Remember these are vectors!). Dipole in an Electric Field: 7 torque on the dipole 7=p@E,|7| = pEsin(0) +> 7 =0whenj || £. The dipole’s associated potential energy is given by, U =—p- E = pEcos(6). > U =Owhenp l E. Gauss’ Law: © = 4x2, where & = f B- dA = fE-dA= ene and calculate E for given applications. Application of Gauss’ Law: We apply Gauss’ Law when an excess (net) charge, placed on an isolated conductor, is lo- cated entirely on the outer surface of the conductor. (Many of these derivations involve the use of symmetry arguments.) 1. E Near the Surface of a Charged Conductor Baz Within the conductor, E = 0. 2. E Due to an Infinte Line of Charge a Xx E= 2Qreor 3. E Due to an Infinite Non-conducting Sheet bax 4. E Outside a Charged Spherical Shell of Radius R B=k4 Forr < R, E=0. 5. E Inside a Uniform Sphere of Charge of Radius R B= ifr Electric Potential Energy: AU = Uy —U; = —-W where W is work done by the electrostatic force. Electric Potential Difference and Electric Potential: = —y,--Wa4u AV =V;-Y=-# = 4! or simply, V = Equipotential Surface: all points in the surface have the same electric potential. Finding V from E: EB.ds Ss AV =- Potential Difference Due to Point Charges: Vaks For a collection of n point charges, Potential Difference Due to a Continuous Charge Dist.: van Electric Potential Energy of a System of Point Charges: U=W=kne Capacitance (two conducting plates): q=CV Capacitance of parallel-plate capacitor: cn Capacitance of an isolated-sphere: C=A4reoR Capacitors in Parallel and in Series: n Ceq = YX CG; (n capacitors in parallel) i=1 n => z (n capacitors in series) Pontential Energy and Energy Density of Capacitor: ~~ ldap U= 30 = 3CV us $6.5" Dielectrics: If the space inside a capacitor is filled with a dielectric material, replace €, with Ke (K = dielectric con- stant). Current: The unit of current is the Ampere, A. i-4 Current Density: i=f Jad Drift Speed of Charge Carriers: F = (ne)uy where vz is the drift speed for n charge carriers. Resistance: The unit of resistance is the Ohm, 2. Resistivity (9) and Conductivity (c): p=s= E=pl For a conducting wire of length L and cross-sectional area A, R= pk Power: P = iV (rate of electrical energy transfer) Power ina Resistor: P =i?R = Y% (esistive dissipation) EMF: = oe =iR Circuit Rules: Loop Rule: the algebraic sum of the changes in potential en- countered in a complete traversal of any loop of a circuit must be zero. Junction Rule: by conservation of charge, the sum of the cur- rents entering any junction must be equal to the sum of the currents leaving that junction. Power ina Battery: the rate at which chemical energy changes is given by Pemg =i€