Equations Paper 2 Explained Flashcards by Daniel Mawson

What is the equation for orbital velocity of an object orbiting in a gravitational field (satelite orbiting a planet)?

V_orb = (GM/r)^1/2

G - gravitational constant (Nm²kg^-2)
M - mass of object creating the field (kg)
r - radius of the orbit from the centre of M (m)

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What is the equation for potential energy at a point in gravitational fields?

E_p = GMm/r = v * m

E_p - gravitational potential energy (J)
G - gravitational constant (Nm²kg^-2)
M - mass of the object creating the field (kg)
m - mass of the object in the field (kg)
v - gravitational potential at that point in the field (J/kg)

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What is the equation for gravitational field strength below the surface of the object creating the field (inside a planet)?

g = 4/3 πpGR

g - gravitational field strength (N/kg)
p - density (kgm^-3)
G - gravitational constant (Nm²kg^-2)
R - distance from centre of sphere to the object (m)

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What is the equation for escape velocity of an object thats in a gravitational field (ball on a planet)?

V_esc = (2GM/r)^1/2

G - gravitational constant (Nm²kg^-2)
M - mass of object creating the field (kg)
r - distance from the centre of mass of M to where the object is starting from (m)

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What formula is used for a substance which changes temperature, in order to find the energy change and what do the symbols mean?

Q = mc θ
Q - the energy input (heat) needed in J
m - mass of the substance in kg
c - specific heat capacity J kg^-1 K^-1
θ - change in temperature in K

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What is the formula for a substance changing state and the energy released and what do the symbols mean?

Q = ml
Q - the energy input needed to change state in J
m - mass of the substance in kg
l - specific latent heat of fusion or vaporisation in J Kg^-1

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What is the equation relating the time of an orbit and the radius of an orbit?

GMT²=4π²r³

G - gravitational constant (Nm²kg^-2)
M - mass of the object creating the field (kg)
T - time period of orbit (s)
r - radius of the orbit from the centre of mass of M (m)

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How is the work done on an object found in gravitational fields and what are the symbols for the equation used?

ΔW = mΔV

W - work done on the object (J)
m - mass of the object which is having work done on it
V - change in potential of the object

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What is the equation for electric potential energy in electric fields?

E_p = 1/4πε₀ * Qq/r = v * q

E_p - electric potential energy (J)
ε₀ - permittivity of free space (Fm^-1)
Q - charge of the charge creating the field (C)
q - charge of the charge in the field (C)
r - distance q is from Q (m)
v - electric potential at that point (JC^-1)

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What formula is used for a charge moving in a uniform electric field?

F = EQ

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What is the formula for gravitational potential and what does this give us?

V = GM/r
This gives gravitational potential at a point

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What are the capacitor charging equations?

Q = Q₀(1-e^-t/RC) Q₀= final charge

V = V₀(1-e^-t/RC) V₀ = final voltage

I = I₀(1-e^-t/RC) I₀ = inital current

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What are the capacitor discharging equations?

Q = Q₀e^-t/RC Q₀= initial charge

V = V₀e^-t/RC V₀= initial voltage

I = I₀e^-t/RC I₀= initial charge

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What are the formulas for gravitational field strength at a point?

g = GM/r²
g = F / m

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What is the equation for the radius of the path of a charged particle moving in a magnetic field?

r = mv/BQ

r - radius of circular path (m)
m - mass of particle (kg)
B - magnetic flux density (T)
Q - charge of the moving particle (C)
v - linear velocity of the moving particle (ms^-1)

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What is the equation for the velocity that will be selected in a mass spectrometer (where magnetic force = electric force)?

v = E/B

v - velocity of particle that will be selected (ms^-1)
E - electric field strength (NC^-1)
B - magnetic flux density (T)

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What is the formula for electric potential and what must you know when using it

V = 1/4πε₀ Q/r
This is electric potential at a point

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What is the standard formula for capacitance and what do the symbols mean?

C = Q/V
From the definition of capacitance which is the charge stored per unit voltage
Q - charge across the capacitor (C)
V - potential difference across the capacitor (V)
C - capacitance of the capacitor (F)

What is the more edgy formula for capacitance and what do the symbols mean?

C = Aε₀ε_r / d
C - Capacitance of capacitor (F)
A - Cross-sectional area of the plates overlap (m²)
ε₀ - permittivity of free space (F/m)
ε_r - relative permittivity (no units)
d - distance between the plates (m)

What are the formulas for energy stored by a capacitor?

E = 1/2 * QV = 1/2 * CV² = 1/2 * Q² / C
All values represent that of which is across the capacitor

What is the time constant formula?

T = RC
T - time taken for charge to fall to 37% of its original value
R - Resistance in the circuit
C - Capacitance of the capacitor

How is the force on a current due to a magnetic field found?

F = BIL (sinθ)
Use sinθ to get perpendicular length to the field

How is the force on a moving charge in a magnetic field calculated?

F = BQv
when v is the velocity of the charge

What is the formula for the torque of a coil rotating in a DC motor?

Torque (Nm) = BILNd

N - number of coils
d - distance between coplanar forces
L - length of coil

This isn’t on the formula sheet

How do you calculate magnetic flux?

Φ = BA Φ - magnetic flux (Wb) B - magnetic flux density which should be resolved perpendicular to the area A - Area which flux is passing through

How do you calculate flux linkage?

Using Φ = BA —> NΦ = NBA NΦ - Flux linkage (Wb turns) B must be perpendicular flux density to the coils

What is the standard formula for the magnitude of an induced emf?

ε = N * ΔΦ/Δt ε - induced emf (V) Other side of formula is change in flux linkage

What is the formula for flux linkage in a rotating coil?

NΦ = BAN cos (wt) **OR** cos (θ)

What is the formula for the magnitude of an induced emf in a rotating coil?

ε = BAN ω sin ωt t- time the coil has been turning for This is the negative derivative of the flux linkage formula as emf is the negative gradient

What is the formula for I_rms and what does this actually mean?

I_rms = I₀ / root 2 I_rms is the DC supply which would provide the same average power per cycle as the AC supply

What is the formula for V_rms and what does this actually mean?

V_rms = V₀ / root 2 V_rms is the DC supply which would provide the same average power per cycle as the AC supply

What is the standard transformer equation and can it only be used in certain situations?

N/N₂ = V/V₂ Can be used **regardless of efficiency**

How should you fill in values for the efficiency of transformers equation?

For the efficiency equation, write efficiency as a decimal if this is known and if not, then when solving for the efficiency note that the answer will be in decimal form

What do V_p and V_s represent in transformer equations?

V_p - Voltage in the **primary coil** V_s - Voltage in the **secondary coil**

Can the formula N = N₀e^-λt be written in any other way?

Yes, can use A (activity) or C(Count rate) instead of N (A = A₀e^-λt) (C = C₀e^-λt) λ - decay constant t - time since initial decay

What is the bog standard activity formula and what does it mean? How else can activity be expressed?

A = λN Activity is the number of unstable nuclei (N) multiplied by the decay constant Activity can also be denoted by ΔN/Δt

What is the formula for the radius of a nucleus and what do the symbols man!

R = R₀A^1/3 R - Radius of nucleus A - Activity (Bq) R₀ - Radius of a hydrogen nucleus

What formula links gravitational field strength and the force due to gravity and what does the mass in the equation represent?

g = F / m m is the mass of the object which is worked upon by the field (gravitational field strength is independent of the mass of the object in the field)

How is the work done on an object found in electric fields and what do the symbols mean?

ΔW = QΔV W - Work done on the object by the field (J) Q - Charge thats in the field (C) V - Change in potential (J/C)

What is the formula for the electric field strength in a radial field and what must you know when using it?

E = 1/4πε₀ Q/r² This is the field strength at a point

What does g = Δv / Δr tell you?

Field strength **over short distances**

For w = qv and w = mv, what do q and m mean?

q and m are the charges/masses that are **acted on by the field**

What is the equation for work done compressing a gas?

W = PΔV W - Work done compressing or decompressing P - Pressure that the gas is constantly at ΔV - Change in volume of the gas