Electric Charge and Coulomb's Law
- Electric charge is quantized: q = n*e, where e = 1.602 x 10^-19 C
- Coulomb's law: F = k*q1*q2/r^2 (k = 8.99 x 10^9 N*m^2/C^2)
- Like charges repel, opposite charges attract
- Superposition: net force is the vector sum of individual forces
- Permittivity of free space: epsilon_0 = 8.854 x 10^-12 F/m
- k = 1/(4*pi*epsilon_0)
Electric Fields
- Electric field: E = F/q (force per unit positive test charge, N/C or V/m)
- Point charge field: E = k*Q/r^2 (directed radially outward from positive charge)
- Field lines: point in the direction of force on a positive charge
- Gauss's law: integral of E*dA = Q_enclosed/epsilon_0
- Uniform field between parallel plates: E = V/d (voltage divided by plate separation)
- Electric potential: V = k*Q/r (scalar quantity, volts)
- Potential energy: U = q*V = k*q1*q2/r
Capacitance
- Capacitance: C = Q/V (farads, F)
- Parallel plate: C = epsilon_0*A/d (A = plate area, d = separation)
- With dielectric: C = kappa*epsilon_0*A/d (kappa = dielectric constant)
- Energy stored: U = (1/2)*C*V^2 = Q^2/(2*C)
- Series: 1/C_total = 1/C1 + 1/C2 + ...
- Parallel: C_total = C1 + C2 + ...
Magnetic Fields
- Magnetic force on a moving charge: F = q*v x B (cross product; magnitude = qvB*sin(theta))
- Force on a current-carrying wire: F = I*L x B (magnitude = BIL*sin(theta))
- Biot-Savart law: dB = (mu_0/(4*pi)) * (I*dL x r_hat)/r^2
- Permeability of free space: mu_0 = 4*pi x 10^-7 T*m/A
- Magnetic field of a long straight wire: B = mu_0*I/(2*pi*r)
- Magnetic field inside a solenoid: B = mu_0*n*I (n = turns per unit length)
- Ampere's law: integral of B*dL = mu_0*I_enclosed
Faraday's Law and Inductance
- Faraday's law: EMF = -N*(d_Phi_B/dt) (induced voltage from changing magnetic flux)
- Magnetic flux: Phi_B = B*A*cos(theta)
- Lenz's law: induced current opposes the change that produced it
- Self-inductance: V = -L*(dI/dt) (L in henries, H)
- Energy stored in inductor: U = (1/2)*L*I^2
- Mutual inductance: M = k*sqrt(L1*L2) (k = coupling coefficient)
Electromagnetic Waves
- Speed of light: c = 1/sqrt(mu_0*epsilon_0) = 3 x 10^8 m/s
- Relationship: c = f*lambda (frequency times wavelength)
- EM spectrum: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma
- E and B fields are perpendicular to each other and to the direction of propagation
- Intensity: I = P/A = (1/2)*c*epsilon_0*E_max^2