Wright State University Lake Campus/2018-9/Phy2410/Equation sheet

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Also available as File:Wsul file pdf 04.pdf


2.5 Electric charges and fields

8.85×10−12 F/m = vacuum permittivity.

e = 1.602×10−19C: negative (positive) charge for electrons (protons)

= 8.99×109 m/F



= field above an infinite plane of charge.

Find E

is the electric field at the field point, , due to point charges at the source points, , and points from source points to the field point.


2.6 Gauss's law:

= electric flux


Surface Integrals

Calculating and with angular symmetry
Cyndrical: .  Spherical:

More Gauss Law

Calculating and with angular symmetry
Cyndrical: .  Spherical:


2.7 Electric potential The alpha-particle is made up of two protons and two neutrons.

= electric potential

= change in potential energy (or simply )

Electron (proton) mass = 9.11×10−31kg (1.67× 10−27kg). Elementary charge = e = 1.602×10−19C.

=kinetic energy. 1 eV = 1.602×10−19J

near isolated point charge

Many charges: .

2.8 Capacitance

defines capacitance.

where A is area and d<<A1/2 is gap length of parallel plate capacitor


= stored energy

= energy density


2.9 Current and resistors

Electric current: 1 Amp (A) = 1 Coulomb (C) per second (s)

Current=, where

= (density, charge, speed, Area)

where =current density.

= electric field where = resistivity

, and ,

where is resistance

and Power=

2.10 Direct current circuits

where =internal resistance and =emf.


Kirchhoff Junction: and Loop:

Charging an RC (resistor-capacitor) circuit: and where is RC time, and .

Discharging an RC circuit: and


2.11 Magnetic forces and fields

cross product

, ,
Magnetic force: .
=EXB drift velocity
Circular motion (uniform B field): Period=

Hall effect

Dipole moment=. Torque=. Stored energy=.
Hall field =
Lorentz force =

2.12 Sources of magnetic fields

Free space permeability T·m/A
Force between parallel wires
Biot–Savart law
Ampère's Law:
Magnetic field inside solenoid with paramagnetic material = where = permeability

(we skip T6 because it was a review of previous chapters)


2.13 Electromagnetic induction

Magnetic flux
Motional if
Electromotive "force" (volts)
rotating coil

2.14 Inductance

Unit of inductance = Henry (H)=1V·s/A

Mutual inductance: where =flux through 1 due to current in 2. Reciprocity


, , Stored energy=

in LR circuit where .

in LC circuit where

2.15 Alternating current circuits

AC voltage and current if
RMS values and
Resistor where
Capacitor where
Inductor where
RLC series circuit where and
Resonant angular frequency
Quality factor
Average power
Transformer voltages and currents


3.2 Geometric optics and image formation


relates the focal length f of the lens, the image distance S1, and the object distance S2. The figure depicts the situation for which (S1, S2, f) are all positive: (1)The lens is converging (convex); (2) The real image is to the right of the lens; and (3) the object is to the left of the lens. If the lens is diverging (concave), then f < 0. If the image is to the left of the lens (virtual image), then S2 < 0 .

Displacement current in capacitor.svg

2.16 Electromagnetic waves

Displacement current where is the electric flux.

Maxwell's equations:


Poynting vector =energy flux

Average intensity

Radiation pressure (perfect absorber) and (perfect reflector).