Download Magnetic Force on an electric current

Electric Power
Magnetic Force on an electric current:
F= nBIl(sin)
F = magnetic force on an electric current [N],
n = number of current-carrying wires,
B = magnetic field (strength) caused by magnets around the wires [T],
I = current travelling through the wires [A],
l: length of the wires [m],
= angle between the current and the magnetic field [o]: sin(90o)= 1, sin(0o)= 0,  F┴= nBIl, F║= 0.
Right-Hand Grip Rule: Imagine that you grab the wire with your right hand so that your thumb is in
the direction of the current (I), your fingers point in the direction of the magnetic field (B) it induces.
‘I’ is the conventional current, i.e., opposite to electron flow!
‘B’ is the magnetic field from N to S created by the current.
Right-Hand Slap Rule: With your flat, open right hand, when your fingers point in the direction of the
magnetic field (B), and your thumb points in the direction of the current (I), then the magnetic force
(F)on the current is in the direction of you palm: ‘slap’.
‘I’ is the conventional current, i.e., opposite to electron flow!
‘B’ is the magnetic field from N to S that is affecting the current.
‘F’ is the magnetic force on the current caused by the interaction of the magnetic field affecting the
current and the magnetic field created by the current.
Magnetic Flux:
 = BAsin,
 = magnetic flux (amount of ‘field lines’ passing through an area) [Wb = webers]
B = magnetic field (strength) [T = teslas]
A = area being considered (e.g., area of a loop)= [m2]
= angle between the field and the area [o]: sin(90o)= 1, sin(0o)= 0, .: ┴ = BA = max, ║= 0 = min,
Faraday’s Law:
av = -n/t,
av = the average emf (voltage) induced in the ends of the loop of wire [V].
= the change in flux (= f inal – initial) due to any of; B, A, or [Wb].
t = the time interval in which the change in flux took place [s].
n = number of loops in the coil, -ve indicates direction due to Lenz’s law.
Alternating Current:
It= A∙sin(2∙∙f∙t)
It = conventional current at time = t [A =amperes],
f = frequency [Hz = hertz]= cycles per second [s-1]. T: period = time required for one cycle [s] = 1/f.
t = time [s]
A = amplitude of induced current [A =amperes] = magnitude from zero to maximum (peak).
RMS and Peak Values:
Vrms = Vpeak/√2, AND Irms = Ipeak/√2,
p-p: peak-to-peak = magnitude from maximum to minimum e.g., Vp-p = 2Vp.
rms: root mean square of values: xrms =√( (xav–x)2) = average magnitude of a variable value
P(Vrms) = P(VDC): Vrms = VDC (for equivalent DC power).
P(Irms) = P(IDC): Irms = IDC (for equivalent DC power).
Electric Power:
P= IV = U/t
P = power transformed by device [W = watts]
I = conventional current through the device [A =amperes]
V = voltage drop across the device [V = volts]
t = time taken to transmit charge or transform energy [s]
U = electrical potential energy associated with each transmitted charge [J]
Electrical Dissipation (Transmission Losses):
V= IR
V = voltage dissipated (lost) across a resistance (e.g., in a transmission wire) [V]
I = current passing through a resistance (e.g., in a transmission wire) [A]
R = resistance of a resistance (e.g., in a transmission wire) []
Power Loss:
Ploss= I2R
Ploss = power dissipated (lost) at a resistance (e.g., in a transmission wire) [W]
I = current passing through a resistance (e.g., in a transmission wire) [A]
R = resistance of a resistance (e.g., in a transmission wire) []
Transformer Action:
np /ns = Vp /Vs = Is/Ip
np = number of turns in the primary coil
ns = number of turns in the secondary coil
Vp = voltage across the primary coil
Vs = voltage across the secondary coil
Ip = current through the primary coil
Is = current through the secondary coil
N.B. Transformers with np > ns, are step-down, np < ns, are step-up.
Light & Matter Formulae
The Wave Equation:
v = f, v = x/t = /T = f
v = velocity of the wave [ms-1]
For light in a vacuum v = c =3.0x108 ms-1,
 = wavelength of the wave [m] Distance between subsequent corresponding points on a wave
f = frequency of the wave [Hz, s-1] = 1/T Number of wavelengths passing a point each second
T = period of the wave [s] = 1/f
Time for one wavelength of the wave to pass through a point
Constructive Interference:
pdC = nC,
nC = 0, 1, 2 …
pdC = path difference between two wave trains that constructively interfere [m]
Difference in distance travelled from two points to an antinode.
nC = number of bright (constructive interference) bands from the central bright band
nC = 0, 1, 2 …; constructive interference; waves meet completely in-phase
= wavelength of monochromatic light passed through an obstacle [m]
Destructive Interference:
pdD = (nD – ½),
nD = 1, 2, 3 …
pdD = path difference between two wave trains that destructively interfere [m]
Difference in distance travelled from two points to a node.
nD = number of dark (destructive interference) bands from the central bright band
nD = 1, 2, 3 …; destructive interference; waves meet completely out-of-phase
= wavelength of monochromatic light passed through an obstacle [m]
Diffraction Geometry:
pdx/w ≈ Wx/D
sinx = pdx/w, & Wx/D = tanx, & tan ≈ sin
x = angle between the centre line & a line from centre of slits to a point of interest ‘x’ [o]
pdx = path difference to a point of interest, ‘x’ [m], normally either a node, nD, or an antinode, nC [m]
w = width of the distance between the centre of the slits or of the obstacle [m]
Wx = width of the gap on the screen between the centre line and the point of interest, x, [m]
D = distance between the slits or obstacle and the screen [m]

Extent of Diffraction:
sinx  /w, pd  
x = angle between the centre line & a line from centre of slits to a point of interest ‘x’ [o]
w = width of the distance between the centre of the slits or of the obstacle [m]
= wavelength of monochromatic light passed through an obstacle [m]
Photon Energy:
EP= hf,
EP = electromagnetic energy of a single photon (light particle) [J, eV]
h = plank’s constant = 6.63 ×10−34 Js = 4.1 ×10-15 eVs.
f = frequency of incident monochromatic light (a single photon) [Hz, s-1]
Electronvolt:
1 eV = 1.602 x10-19 J
eV = unit of energy equal to the joules (J) of energy need to accelerate an electron through 1 volt
Accelerating an Electron:
EKe = eV,
EKe = kinetic energy change of electron= work done by voltage to change an electron’s kinetic energy
e = the magnitude of charge on an electron 1.6 x10-19 C
V = the voltage used to change the kinetic energy of the electron [V]
Electron Energy:
EKmax = ½mevmax2 = eV0,
EKmax = maximum kinetic energy of photoelectrons [J, eV]
me= mass of an electron = 9.1 x10-31 kg
vmax = maximum velocity of photoelectrons [ms-1]
e = the magnitude of charge on an electron 1.6 x10-19 C
V0 = stopping voltage, the voltage used to change the kinetic energy of the most energetic electrons [V]
Ionisation Energy:
EK = EP - EI
EK = kinetic energy of photoelectrons, electrons released by photons [J, eV]
EP = photon energy of incident monochromatic light [J, eV]
EI = ionisation energy required to release an electron from an atom [J, eV]
Photoelectric Effect:
EKmax = hf – W,
EKmax = maximum kinetic energy of photoelectrons [J, eV]
h = plank’s constant = 6.63 ×10−34 Js = 4.1 ×10-15 eVs.
f = frequency of monochromatic light (a single photon) [Hz]
W = work function, energy to ionise (release) the most energetic electrons in an atom = (EImin) [J, eV]:
Graph: y= mx+c :: EKmax= hf–W | y = EKmax | m = h = W/f0 | x = f | c = –W | -c/m = W/h = f0 |
Emission & Absorption:
E = hf, E = Ef – Ei,
E = change in energy state of an orbital electron = Ef – Ei = final minus initial energy state [J, eV]
h = plank’s constant = 6.63 ×10−34 Js = 4.1 ×10-15 eVs.
f = frequency of monochromatic light (a single photon) [Hz]
Photon & De Broglie Wavelength:
p = mv = hf/c = h/
p = momentum of a photon OR a particle such as an electron [kg ms-1]

m = mass of a particle such as an electron NB photons have no mass [kg]
v = velocity of a particle such as an electron [ms-1]
h = plank’s constant = 6.63 ×10−34 Js = 4.1 ×10-15 eVs.
f = frequency of monochromatic light (a single photon) [Hz]
c = speed of light in a vacuum = 3.0x108 ms-1,
= wavelength of monochromatic light OR of an particle such as an electron [m]
Electron Standing Wave Orbit:
2r = nnh/mv,
n = wavelength number, r = orbit radius [m], mv = electron momentum [kg ms-1]

Sound
Universal Wave Equation:
v = f, f = 1/T
v = velocity of sound in an elastic medium, e.g., air = 340 ms-1 unless specified [ms-1]
 = wavelength of sound in medium: distance between subsequent corresponding points on a wave [m]
f = frequency of sound due to a source [Hz] = number of oscillations per second [s-1].
T = period of sound due to a source = time taken for one oscillations [s].
Resonance
Even Oscillators
n (even)= 2ℓ/(n+1), m = n + 1
n (even)= wavelength of the nth overtone of the even oscillator [m]
ℓ = length of an even oscillator [m]
n = whole number order of the overtone, where n= 0 is the fundamental tone or 1st harmonic
m = whole number order of the harmonic, where m = 1 is the 1st harmonic or fundamental tone
N.B. all harmonics are possible in an even oscillator
Odd Oscillators
n (even)= 4ℓ/(2n+1), m = n + 1
th
n (even)= wavelength of the n overtone of the odd oscillator [m]
ℓ = length of an odd oscillator [m]
n = whole number order of the overtone, where n= 0 is the fundamental tone or 1st harmonic
m = whole number order of the harmonic, where m = 1 is the 1st harmonic or fundamental tone
N.B. only odd harmonics are possible in an odd oscillator
Sound Intensity
I = P/A,
Asphere= 4r2
I  1/r2,
I1r12 = I2r22
-2
I = intensity of sound at a specific distance from a source [Wm ]
P = power of sound at a specific distance from a source [W]
A = cross-sectional area across which the power of a sound is incident [m2]
Asphere = area of sound if it is able to spread out unimpeded by obstacles in a sphere.
r = distance (radius) that the intensity of sound is from a source [m]
I1 = original intensity, I2 = changed intensity, r1 = original distance, r2 = changed distance,
NB: as the distance doubles the intensity quarters (inverse square law)
Sound Intensity Level
L = 10log(I/I0), I0=10-12, I = 10(L/10) – 12
L = Sound Intensity Level measured in decibels [dB]
I = Sound Intensity measured in watts per meter squared [Wm-2]
I0 = Sound Intensity at the threshold of hearing, I0=10-12 Wm-2
Change in Sound Intensity Level
ΔL = L2 – L1 = 10log(I2/I1), I2 = I1×10(ΔL/10)
ΔL = Change in Sound Intensity Level measured in decibels [dB]
L1 = Original Sound Intensity Level measured in decibels [dB]
L2 = Changed Sound Intensity Level measured in decibels [dB]
I1 = Original Sound Intensity measured in watts per meter squared [Wm-2]
I2 = Changed Sound Intensity measured in watts per meter squared [Wm-2]
Extent of Diffraction:
sinx  /w
x = angle between the centre line & a line from centre of slits to a point of interest ‘x’ [o]
w = width of a gap or of an obstacle [m]
= wavelength of sound passed around an obstacle or through an gap [m]
/w <<1 = too small, <1 = small, ≈ 1 moderate, >1= large, >>1 = too large