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

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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

  where  

  where  

  = 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

 

  where  

 

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.

  and  

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 

Self-inductance:  

 ,  , Stored energy= 

  in LR circuit where  .

  in LC circuit where  

2.15 Alternating current circuits

AC voltage and current   if  
RMS values   and  
Impedance  
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 .


 

2.16 Electromagnetic waves

Displacement current   where   is the electric flux.

Maxwell's equations:  
 
 
 
 


  and  

Poynting vector  =energy flux

Average intensity  

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