Equations Flashcards
What is the equation for the force on a charged particle subject to an E-field and B-field?
F = force
q = charge
E = electric field
B = magnetic field
v = velocity
What is the equation that relates a particles mass and velocity to the magnetic field that it is in?
q = charge
v = velocity
B = magnetic field
m = mass
R = bending radius
What is the equation for the bending radius of a particle?
R = bending radius
m = mass
v = velocity
q = charge
B = magnetic field
p = momentum
What is the equation for magnetic rigidity?
BR = magnetic rigidity
p = momentum
q = charge
What is the equation for capacitance?
V = voltage
Q = charge
C = capacitance
What is the equation for capacitance when voltage is changing?
V = voltage
t = time
I = current
C = capacitance
What is the equation for the time in a single tube for a standing wave LINAC?
t = time in a single tube
f = frequency
v_i = length of tube
l_i = velocity of particle in the tube
What is the equation for the frequency of the cyclotron?
f = frequency
T = time period
B = magnetic field
q = charge
m = mass
What is the equation for relativistic mass?
m = relativistic mass
γ = Lorentz factor
m_0 = rest mass
What is the equation for cyclotron frequency with relativistic particles?
f = frequency
T = time period
B = magnetic field
q = charge
γ = Lorentz factor
m_0 = rest mass
What is the equation for the Lorentz factor?
v = particle velocity
c = speed of light
What is the equation for the surface area of a spherical cap?
S = surface area
R = sphere radius
h = cap height
What is the equation for the circumference of a spherical cap?
C = circumference
a = cap radius
R = sphere radius
What is the equation for the electric flux through a surface area?
Φ = flux
E = electric field
A = surface area
What is the equation for the transverse flux of an accelerated particle?
Φ_t = transverse flux
E_t = transverse electric field
R = sphere radius
c = speed of light
∆t = time
What is the equation for the transverse electric field of an accelerated particle?
E_t = transverse electric field
q = charge
a = cap radius
ε_0 = permittivity of free space
R = sphere radius
c = speed of light
What is the equation for the transverse magnetic field generated by synchrotron radiation?
B_t = transverse magnetic field
E_t = transverse electric field
c = speed of light
q = charge
a = cap radius
ε_0 = permittivity of free space
R = sphere radius
What is the equation for projected power due to synchrotron radiation?
S = power
E = electric field
H = magnetic field strength
B = magnetic field
µ_0 = permeability of free space
c = speed of light
q = charge
a = cap radius
ε_0 = permittivity of free space
R = sphere radius
What is the equation for the total radiated power due to synchrotron radiation?
S = projected power
c = speed of light
q = charge
a = cap radius
ε_0 = permittivity of free space
What is the equation for the total radiated power due to synchrotron radiation for relativistic particles?
c = speed of light
q = charge
a = cap radius
ε_0 = permittivity of free space
γ = Lorentz factor
What is the equation for the power lost per revolution from a synchrotron light source?
What is the equation for the energy gained by an electron in an x-ray tube?
e = electron charge
∆V = potential difference
What is the equation for the maximum energy of an emitted photon in an x-ray tube?
What is the equation for the characteristic energy of hydrogen?
E_n = characteristic energy
m_e = mass of electron
q_e = electron charge
n = principal quantum number
What is the equation for the characteristic energy of larger atoms?
E_n = characteristic energy
m_e = mass of electron
q_e = electron charge
n = principal quantum number
Z = atomic number
What is the equation for the energy difference when electrons transition between shells?
E_n = characteristic energy
m_e = mass of electron
q_e = electron charge
n_i = initial quantum number
n_f = final quantum number
What is the differential form of the intensity equation?
dI = change in beam intensity
I = original beam intensity
dx = incremental distance
n = number of atoms per unit volume
σ = constant related to the probability of scattering
What is the equation for beam intensity when the linear attenuation coefficient is constant?
I(x) = intensity
I_0 = initial beam intensity
n = number of atoms per unit volume
σ = constant related to probability of scattering
x = position
µ = linear attenuation coefficient
What is the general equation for the linear attenuation coefficient?
I(x) = intensity
I_0 = initial beam intensity
dx = incremental distance
µ = linear attenuation coefficient
What is the relation that described the contribution of the photoelectric effect to the linear attenuation coefficient?
µ = linear attenuation coefficient
ρ = density
Z = atomic number
E = energy
What is the relation that described the contribution of Compton scattering to the linear attenuation coefficient?
µ = linear attenuation coefficient
ρ = density
What is the equation for a 1D Fourier transform?
What is the equation for a 1D inverse Fourier transform?
What is the equation for a 2D Fourier transform?
What is the equation for a 2D inverse Fourier transform?
What is the equation for the projection of a CT scan?
P = projection
I = intensity
I_0 = initial intensity
µ = linear attenuation coefficient
dS = incremental distance
What is the equation for the projection of an image in the rotated plane, using the intensity values calculated by the x-ray CT scanner?
I(S) = intensity
I_0 = initial intensity
P = projection
φ = rotation angle
r = radius
What is the general equation for a projection?
What is the equation for the simulated projections in iterative back projection?
What is the signal to noise ratio for x-ray CT?
N = number of photons
What is the equation for activity?
A = activity
N = number of decays
t = time
λ = decay constant
What are the equations for physical half-life?
N = number of nuclei
t = time
λ = decay constant
τ = half life
What is the equation for effective half-life?
What is the equation for the decay of Mo-99?
N_1 = number of Mo-99 molecules
t = time
λ_1 = decay constant
What is the equation for the build up of Tc-99m?
N_1 = number of Mo-99 molecules
N_2 = number of Tc-99m molecules
t = time
λ_1 = Mo-99 decay constant
λ_2 = Tc-99m decay constant
What is the equation for the spatial resolution of a gamma camera?
R = resolution
l = collimator thickness
d = diameter of septa
z = distance to sample
What is the equation for the FWHM (full width half maximum) for the blurring of the image generated by PET?
D = patient diameter
