PHYS1169/part 1
Equation and units summary 

(Students, note: this is just a study aid, you still need to use your textbook and lecture notes to revise for the exam!!)

Topic	Equations	units	

Vectors	
Vector magnitude in xyz coordinates

The scalar product

A.B = AxBx + AyBy + AzBz = AB cos

The vector product

A x B = (AyBz -AzBy)i  + (AzBx - AxBz)j + (AxBy -AyBx)k

           = AB sin
	
Units depend on what the vector represent (e.g. displacement, velocity, force)	

Electrostatics	
Electric field due to a point charge q at distance r

Force between charge q1 and q2, at distance r

Potential energy of bringing a group of charges together

change in potential between two points in space

Potential due to several point charges:

One "electron-volt" is the energy gained by electron in falling through a potential difference of 1 V:

W = -qDV = - (-e)(1 V) = 1.6 x 10-19 Joule = 1 eV

Calculating the potential from the field

For a distance d in a  direction parallel to a uniform field E:

DV = -Ed    (electric field times distance d)

Newton/Coulomb
            or
      Volts/meter

Newtons

Joules

Joules/Coulomb
or Volt

Volt

eV

Volts

Volts	
Capacitance	
The charge Q on a parallel plate capacitor with potential difference V across it:

Q = CV

C is the capacitance.

The electric field between the parallel plates:

A is the area of the plates,  is charge density /A

Energy stored in a capacitor:

Energy density:

For two capacitors C1 and C2 connected in series, the equivalent total capacitance Ctotal:

For two capacitors C1 and C2 connected in parallel, the equivalent total capacitance Ctotal:

Ctotal = C1 + C2

Coulombs

Newton/Coulomb

Farads

Joules

Joules/m3	

Current and Resistance	
              (Q is charge)

The current per unit cross-section area A is called current density J:

where vd is the drift velocity

Ohm's Law:

V = IR
 
Resistance R

where A and  are area and length of the conductor and  is resistivity of the material.

For two resistorss R1 and R2 connected in parallel, the equivalent total resistance Rtotal:

For two resistorss R1 and R2 connected in series, the equivalent total resistance Rtotal:

Rtotal = R1 + R2

Power:

Kirchhoff's Rules:

Charge on a capacitor C being charged by e.m.f.  through resistor R:

t is time

Charge on a capacitor C being discharged through resistor R:

where Q0  is the initial charge at time t = 0

current in a RC circuit (charging) 	
Amperes

Amperes/m2

Volts

Ohm

ohm

Watts or Joules/sec

Coulombs

Coulombs

Amperes	

Magnetism

	
Force on a charge q moving with velocity v in magnetic field B:

FB = qv x B = 

The radius of charge q moving in a circle in a magnetic field:

Force on a current carrying wire of length L in magnetic field B:

Magnetic field due to a moving charge q:

The magnetic field produced by current element dl:

The total field of a long wire must be found by integration.
(Biot-Savart rule)

Field due to long straight wire at distance R:

Force between two parallel wires separated by distance d, carrying currents i1 and i2:

Ampere's Law

Magnetic field inside an ideal solenoid with n windings per unit length

Newtons

Newtons

Tesla

Tesla

Tesla

Newtons

Tesla

Induction

	
The induced e. m. f.,  , is given by:

 
N is number of turns

For a constant B and a flat loop with area A,
Magnetic flux:

 B  = B.A =  BAcos  (scalar product)

Motional electromotive force:
(Loops moving in and out of magnetic field, rod sliding on rails, with velocity v)

Current in the loop:

Force opposing the motion:

Inductance of a coil of area A and length 

L = 0n2 A

e.m.f. induced in a coil:

Series inductances add:

L = L1 + L2

Parallel inductances add as reciprocals:

current in RL circuit:

energy stored in an inductor:

Volts

Tesla.m2 or Weber

Volts

Amperes

Newtons

Henry

Volts

Henry

Amperes

Joules

Alternating current circuits	
Series circuit

Current:
i(t) = Im sin t

applied voltage:
v(t) = Vm sin (t + )

angular frequency:

 = 2f

Reactances:

XL = L

Voltages across capacitor and inductor
Vc = ImXc
VL = ImXL

Scalar impedance:

The angle between current and applied voltage:

Vm = ImZ

Vrms = IrmsZ

Power:

P = Irms2R = IrmsVrmscos

Resonant frequency:

Amperes

Volts

Rads/sec

Ohm

Ohm

Volt
Volt

Ohm

Volts

Amperes

Volts

Volts

Watts

Rads/sec