Equations

Question 1

What is the equation for the force on a charged particle subject to an E-field and B-field?

Answer 1

F = force
q = charge
E = electric field
B = magnetic field
v = velocity

Question 2

What is the equation that relates a particles mass and velocity to the magnetic field that it is in?

Answer 2

q = charge
v = velocity
B = magnetic field
m = mass
R = bending radius

Question 3

What is the equation for the bending radius of a particle?

Answer 3

R = bending radius
m = mass
v = velocity
q = charge
B = magnetic field
p = momentum

Question 4

What is the equation for magnetic rigidity?

Answer 4

BR = magnetic rigidity
p = momentum
q = charge

Question 5

What is the equation for capacitance?

Answer 5

V = voltage
Q = charge
C = capacitance

Question 6

What is the equation for capacitance when voltage is changing?

Answer 6

V = voltage
t = time
I = current
C = capacitance

Question 7

What is the equation for the time in a single tube for a standing wave LINAC?

Answer 7

t = time in a single tube
f = frequency
v_i = length of tube
l_i = velocity of particle in the tube

Question 8

What is the equation for the frequency of the cyclotron?

Answer 8

f = frequency
T = time period
B = magnetic field
q = charge
m = mass

Question 9

What is the equation for relativistic mass?

Answer 9

m = relativistic mass
γ = Lorentz factor
m_0 = rest mass

Question 10

What is the equation for cyclotron frequency with relativistic particles?

Answer 10

f = frequency
T = time period
B = magnetic field
q = charge
γ = Lorentz factor
m_0 = rest mass

Question 11

What is the equation for the Lorentz factor?

Answer 11

v = particle velocity
c = speed of light

Question 12

What is the equation for the surface area of a spherical cap?

Answer 12

S = surface area
R = sphere radius
h = cap height

Question 13

What is the equation for the circumference of a spherical cap?

Answer 13

C = circumference
a = cap radius
R = sphere radius

Question 14

What is the equation for the electric flux through a surface area?

Answer 14

Φ = flux
E = electric field
A = surface area

Question 15

What is the equation for the transverse flux of an accelerated particle?

Answer 15

Φ_t = transverse flux
E_t = transverse electric field
R = sphere radius
c = speed of light
∆t = time

Question 16

What is the equation for the transverse electric field of an accelerated particle?

Answer 16

E_t = transverse electric field
q = charge
a = cap radius
ε_0 = permittivity of free space
R = sphere radius
c = speed of light

Question 17

What is the equation for the transverse magnetic field generated by synchrotron radiation?

Answer 17

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

Question 18

What is the equation for projected power due to synchrotron radiation?

Answer 18

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

Question 19

What is the equation for the total radiated power due to synchrotron radiation?

Answer 19

S = projected power
c = speed of light
q = charge
a = cap radius
ε_0 = permittivity of free space

Question 20

What is the equation for the total radiated power due to synchrotron radiation for relativistic particles?

Answer 20

c = speed of light
q = charge
a = cap radius
ε_0 = permittivity of free space
γ = Lorentz factor

Question 21

What is the equation for the power lost per revolution from a synchrotron light source?

Answer 21

Question 22

What is the equation for the energy gained by an electron in an x-ray tube?

Answer 22

e = electron charge
∆V = potential difference

Question 23

What is the equation for the maximum energy of an emitted photon in an x-ray tube?

Answer 23

Question 24

What is the equation for the characteristic energy of hydrogen?

Answer 24

E_n = characteristic energy
m_e = mass of electron
q_e = electron charge
n = principal quantum number

Question 25

What is the equation for the characteristic energy of larger atoms?

Answer 25

E_n = characteristic energy m_e = mass of electron q_e = electron charge n = principal quantum number Z = atomic number

Question 26

What is the equation for the energy difference when electrons transition between shells?

Answer 26

E_n = characteristic energy m_e = mass of electron q_e = electron charge n_i = initial quantum number n_f = final quantum number

Question 27

What is the differential form of the intensity equation?

Answer 27

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

Question 28

What is the equation for beam intensity when the linear attenuation coefficient is constant?

Answer 28

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

Question 29

What is the general equation for the linear attenuation coefficient?

Answer 29

I(x) = intensity I_0 = initial beam intensity dx = incremental distance µ = linear attenuation coefficient

Question 30

What is the relation that described the contribution of the photoelectric effect to the linear attenuation coefficient?

Answer 30

µ = linear attenuation coefficient ρ = density Z = atomic number E = energy

Question 31

What is the relation that described the contribution of Compton scattering to the linear attenuation coefficient?

Answer 31

µ = linear attenuation coefficient ρ = density

Question 32

What is the equation for a 1D Fourier transform?

Answer 32

Question 33

What is the equation for a 1D inverse Fourier transform?

Answer 33

Question 34

What is the equation for a 2D Fourier transform?

Answer 34

Question 35

What is the equation for a 2D inverse Fourier transform?

Answer 35

Question 36

What is the equation for the projection of a CT scan?

Answer 36

P = projection I = intensity I_0 = initial intensity µ = linear attenuation coefficient dS = incremental distance

Question 37

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?

Answer 37

I(S) = intensity I_0 = initial intensity P = projection φ = rotation angle r = radius

Question 38

What is the general equation for a projection?

Answer 38

Question 39

What is the equation for the simulated projections in iterative back projection?

Answer 39

Question 40

What is the signal to noise ratio for x-ray CT?

Answer 40

N = number of photons

Question 41

What is the equation for activity?

Answer 41

A = activity N = number of decays t = time λ = decay constant

Question 42

What are the equations for physical half-life?

Answer 42

N = number of nuclei t = time λ = decay constant τ = half life

Question 43

What is the equation for effective half-life?

Answer 43

Question 44

What is the equation for the decay of Mo-99?

Answer 44

N_1 = number of Mo-99 molecules t = time λ_1 = decay constant

Question 45

What is the equation for the build up of Tc-99m?

Answer 45

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

Question 46

What is the equation for the spatial resolution of a gamma camera?

Answer 46

R = resolution l = collimator thickness d = diameter of septa z = distance to sample

Question 47

What is the equation for the FWHM (full width half maximum) for the blurring of the image generated by PET?

Answer 47

D = patient diameter