AP Electricity and Magnetism Equations to memorize Flashcards

Question

Resistance of a wire

Answer 1

R = ρ(L/A) Where ρ is resisitivity L = length A = cross sectional area

Answer 2

B = μ₀I / 2πR

Answer 3

v_f² = v_i² + 2(a)(Δs)

Answer 4

F*_ll* = F_g ∙ sinθ

Answer 5

I = Σ(mr²)

Answer 6

Acceleration

Answer 7

τ = F∙ r_┴ ( torque = force times "lever arm" ) (The lever arm is just the shortest distance between the axis of rotation and the path the force is acting along.)

Answer 8

v = √(v_x² + v_y²)

Answer 9

W_rot = (τ)(Δθ)

Answer 10

∫ (e^u)dx = (1/u’)(e^u) + C

Answer 11

Electric charge and field are zero

Answer 12

V = -L(dI / dt)

Answer 13

EMF = V - IR_int

Answer 14

ФB = A∙B = ABcosθ (Often, in the problems we do, the area vector and the magnetic field will be parallel, so the cosθ is equal to one and thus dropped from the equation.)

Answer 15

1/R_parallel = 1/R₁ + 1/R₂ + 1/R₃….

Answer 16

F_c = ma_c

Answer 17

T = 2π√(L/g)

Answer 18

F_kf = ± μ_kf∙ F_N

Answer 19

∫ k f(x)dx = k ∫ f(x)dx

Answer 20

T = 2π√(I/mgd)

Answer 21

Δs = (v_i)(Δt) + ½(a)(Δt²)

Answer 22

F_E = kq₁q₂ / r²

Answer 23

g = G∙m_p/r_p² (This is pretty much just the Law of Universal Gravitation with the mass of the planet and the radius of the planet plugged in.)

Answer 24

Vc = Vs(1e^{-t / RC}) RC the time constant (tau) (resistance x capacitance) V_s is the supplied voltage

Answer 25

U_g = (-G∙m₁∙m₂)/ r

Answer 26

F_g = (G∙m₁∙m₂ )/ r²

Answer 27

a = dv / dt

Answer 28

Negative of force

Answer 29

P = W / Δt

Answer 30

ФB = E∙A ( In most cases that we will work with at this level, the two will be perpendicular, so the dot product just drops out. )

Answer 31

Change in velocity

Answer 32

∫ (u + v)dx = ∫ (u)dx + ∫ (v)dx + C

Answer 33

d/dx (sin x) = cos x

Answer 34

v = √2Gm / R

Answer 35

K = ½ mv²

Answer 36

a = Δv / Δt

Answer 37

d/dx (cos x) = - sin x

Answer 38

Thumb - direction charge or current is moving Fingers - direction of magnetic field Open palm - direction of force.

Answer 39

Δs = s_f – s_i

Answer 40

U_sp= ½ ks²

Answer 41

∫ (sin x)dx = -cos x + C

Answer 42

v_x = v(cos θ)

Answer 43

v_y = v(sin θ)

Answer 44

C = ε(A/d) ε = permeativity of free space (8.85 x 10^-12 F/m)

Answer 45

dV = -E·ds

Answer 46

∫ f(xⁿ)dx = (xⁿ⁺¹/n+1) + C

Answer 47

ΔL=0 if and only if Στ_ext = 0

Answer 48

EMF = -N(dФB / dt) ( N is the number of loops )

Answer 49

Rotate counterclockwise from the first vector to the second vector

Answer 50

W = ∫(F)(ds)

Answer 51

Στ = I∙α ( α is alpha, or angular acceleration )

Answer 52

K_rot = ½∙I∙ω²

Answer 53

F = IL x B

Answer 54

∫ (1/x)dx = ln|x| + C

Answer 55

L = rmv ## Footnote also L = Iω

Answer 56

J = Δp ( Impulse = change in momentum )

Answer 57

v_sat = √(G∙m_centeral / r_orbit)

Answer 58

d/dx (u + v) = du/dx + dv/dx

Answer 59

Vc = Vi(e^{-t / RC}) RC the time constant (tau) (resistance x capacitance) V_i is the intital voltage on the capacitor

Answer 60

F_sf ≤ ± μ_sf ∙ F_N

Answer 61

∫ (cos x)dx = sin x + C

Answer 62

W = (F*_ll*)(Δs)

Answer 63

ΣW = ΔK ( make sure you remember this one )

Answer 64

v = ds / dt

Answer 65

Vectors point how a test mass would accelerate

Answer 66

I = dQ / dt

Answer 67

I = I_cm + md² ( If you know the moment of interia of an object rotating around its center of mass I_cm but the object is instead rotating around an axis that is distance "d" from the center of mass, the new rotational intertia can be found with this equation )

Answer 68

v_avg = Δs / Δt

Answer 69

Change in position

Answer 70

ΣU + ΣK + ΣEth = constant for a closed system ( this is a simplification, as it does not include chemical potential energy, electrical potential energy, etc. )

Answer 71

T = 2π√(m/k)

Answer 72

V_L = V₀(e^{-Rt / L})

Answer 73

F = qv x B

Answer 74

S = distance / time

Answer 75

ΔV_loop = 0

Answer 76

C = κε(A/d) κ = dielectric constant

Answer 77

J = ∫(F)(dt)

Answer 78

ΣF = ma ## Footnote (don't forget how many times you could get 1 point on a free response simply by writing this down)

Answer 79

v_avg = (v_i + v_f) / 2

Answer 80

F_N = F_g ∙ cosθ

Answer 81

U_E = kq₁q₂ / r

Answer 82

1/C_series = 1/C₁ + 1/C₂ + ….

Answer 83

V = kq₁ / r

Answer 84

Σp_i = Σp_f if ΣF_ext = 0 ( With no external forces, the momentum of a system will be conserved ) ( This is true for both linear and angular momentum )

Answer 85

Vectors pointed how a positive test charge would accelerate

Answer 86

P = ΔE / Δt

Answer 87

C_parallel= C₁ + C₂ + C₃ …. (Note: this is sort of opposite the rule for resistors in parallel. )

Answer 88

d/dx (uv) = v(du/dx) + u(dv/dx)

Answer 89

Point RH thumb in the direction of the current, RH fingers curl in the direction of the resulting magnetic field.

Answer 90

I = kMR² ^{( k = the number of these objects )}

Answer 91

Q_enc = ε₀ФE

Answer 92

ds = r∙dθ

Answer 93

τ = RC τ is tau R = resistance C = capacitance

AP Electricity and Magnetism Equations to memorize Flashcards

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