Physics 259 equations to remember

E of Line of charge (finite)

E=kλL/(Z(L²/4+z²)^(1/2))

E of infinite line of charge

2Kλ/z

Disk

K(2πδ-(2πδz/(R²+z²)^1/2)

E of ring

KQZ/( R²+z²)^(3/2) OR

K2πλRZ/( R²+z²)^(3/2)

Infinite sheet

E =δ/2ε

Plates

E =δ/ε

Dipole

P =qd

Torque of dipole

τ = P x E

Magnitude of torque

τ = |p||E|sinθ

Flux

Φ = E•A or integral of EA

Gauss’s law

(Qenc/ε)=integral E • dA

Is the flux a scalar or vector

Scalar

Is dipole moment scalar or vector

Vector

What is the flux if perpendicular to electric field

0

What is Torque if parallel to electric field

0

What shapes is the E constant and EA can be applied

Sphere, cylinder and planar

Sphere inside flux

E= ρr/3ε

Sphere outside flux

E = ρR³/(3εr²)

What is the electric field going through a cylinder horizontally

E =λenc/(2πε)

Volume of sphere

4/3πr³

Blume of cylinder

2πrl

Electric field outside cylinder

δR/ rε

Cylinder inside flux

E=0

Plane flux

δ/2ε

B field in straight wire

B =μI/ 2πr

B field in infinite sheet

B = μ J/2

Pitch distance

P =vT

EMF induced

ε= VBL or ε= IR

Voltage in capacitor in arc

V(t) = ε(1-e^(-t/RC))

Voltage of resistor in RC

Vr(t) = εe^(-t/RC)

Energy in capacitor

U(t) =U e^(-2t/RC)

Current density J

J = I/A= ne(e)d

Electric field in terms of current density

E= pJ

Hall voltage?

ΔVH= IBd/nqA