Physics 2 Test 2

Electric Potential Energy

ΔU=qΔV

Electric Field-Potential Relationship

E=−∇V

Parallel-Plate Capacitor: Capacitance

C= ε0​A/d​

Parallel-Plate Capacitor: stored energy

U = ½ ​CV² = ½ ​Q²/C = ½ ​QV

RC Circuit Time Dependence, Charging: Charge

Q(t)=Q_max​(1−e^-t/RC)

RC Circuit Time Dependence, Charging: Voltage of the Capacitor

V_C​(t)=emf(1−e^-t/RC)

RC Circuit Time Dependence, Charging: Voltage of the Resistor

V_R​(t)=emf(e^-t/RC)

RC Circuit Time Dependence, Charging: Current

I(t) = (emf/R)(e^-t/RC)

RC Circuit Time Dependence, Discharging: Charge

Q(t) = Q_⁰(1 - e^-t/RC)

RC Circuit Time Dependence, Charging: Q_max

Q_max = C(emf) = C(V)

RC Circuit Time Dependence, Discharging: Voltage of Capacitor

V_C(t) = V₀(e^-t/RC)

RC Circuit Time Dependence, Discharging: Current

I(t) = (V₀/R)(e^-t/RC)

Resistance

R=ρ(L/A)​

Resistivity

ρ=1/ς

Magnetic Field from a Long Straight Wire

B= μ₀I​/2πr

Magnetic Field at the Center of a Circular Loop

B = μ₀I/2R​

Magnetic Force on a Current-Carrying Wire

F=IL×B

Magnetic Force on a Moving Charge

F = ∣q∣vBsinθ = qv×B

Circular Motion of a Charged Particle in a Magnetic Field: radius

r = mv/∣q∣B

Circular Motion of a Charged Particle in a Magnetic Field: Period

T = 2πm​/|q|B

Velocity Selector Condition

v = E/B

Motional emf

emf=BLv

Magnetic Dipole Moment (directional include vectors)

μ​=IA (in direction of B when on the axis of the dipole)

Torque on a Magnetic Dipole

τ=μ​×B

Power in a Circuit

P = I²R = V²/R = IV

Current Density and Drift Speed Relationship

J = nqvd_d ; I = nqv_dA

Hall Effect Relationships

E_H=v_d​B, V_H = E_Hw = IB/nqt

Definition of Potential Difference

ΔV=−∫E⋅dl

Density of Current Flow Relationship to Total Current

I=∫J⋅dA

Density of Current Flow Relationship to Total Current: J is uniform and parallel to the surface normal

I = JA → I = nqv_dA

Uniform Electric Field

E = v/d, V = ED, d = v/E

Uniform Electric Field: Potential Difference

E = - ΔV/Δd = (V_high - V_low)/(d_f - d_i)

Electric Potential for a Point Charge

V = kQ/r

Parallel-Plate Capacitor: Capacitance w/ Dielectric constant

C= kε₀​A/d​

Dielectric Constant

k = C/C₀ = ε/ε₀

Permittivity

ε = C(d/A)

Electron current

i = nAv_d = nAuE

Superposition: E_field

E_net = E₁ + E₂

Superposition: B_field

B_net = B₁ + B₂

Biot-Savart Law

ΔB = (μ₀/4π)(qv×r_unit/r²)

Biot-Savart Law: Single Charge

B = (μ₀/4π) ​​∣q∣vsinθ/r²​

Loop Rule

∮E⋅dl=0 or ∑ΔV = 0

Ohm’s Law

V = IR

Node Rule

I_in = I_out

Work-Energy Principle

ΔE = ΔW_surr = F_xΔx

Vector into Page

Circle and cross

Vector out of page

Circle and dot

Charge in Capacitor when fully charged

ΔV_C = emf

Finding B_wire from B_earth/deflection angle

tan(θ) = B_w/B_e

R in series

R_eq = R₁ + R₂ + R₃ + …

R in Parallel

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃

Fnet, perpendicular

mv²/R

Electric Force

F_ele = |q|E