Physics Summary Notes

Chapter 21: Grounded Non-Polar Molecules

• Non-Polar Molecules:

  • No permanent dipole moment

  • May have induced dipole moment when a charged object is nearby

• Conductors:

  • Connected to Earth, allowing for charge movement

• Coulomb's Law:

  • Formula for the electric force between two point charges:
    $$Fe = rac{k imes q1 imes q_2}{r^2}$$
    where:

  • $k$$$k$$ = Coulomb's constant, $$q1$and$$$ and $$q2$are the magnitudes of the charges, and$$$ are the magnitudes of the charges, and $$r$$ is the distance between the charges.

  • Fundamental unit of charge is the Coulomb (C), where $1 ext{C} = 1.602 imes 10^{-19} ext{e}$$$1 ext{C} = 1.602 imes 10^{-19} ext{e}$$.

• Electric Field (E):

  • Created by charges, with forces exerted on other charges.

  • Electric field is defined as:
    $E = rac{F_e}{q}$$$E = rac{F_e}{q}$$

  • E vector indicates both magnitude and direction.

• Charge Conservation:

  • The net charge is constant; it can be transferred but not created or destroyed.

• Electric Field Lines:

  • Visual representation of electric fields. The density of lines indicates the strength of the field.

• Polar Molecules:

  • Have an unequal distribution of charges, resulting in a permanent dipole moment.
    ;

• Dipole Moment (P):

  • Defined as:
    $p = q imes d$$$p = q imes d$$
    where $d$$$d$$ is the distance between the charges.

Chapter 22: Electric Flux

• Electric Flux:

  • Defined as the number of electric field lines passing through a given area.

  • Given by the equation:
    $ext{Flux} = E imes A imes ext{cos}( heta)$$$ ext{Flux} = E imes A imes ext{cos}( heta)$$
    where $A$$$A$$ is the area, and $heta$$$ heta$$ is the angle between the field and the normal to the area.

• Gauss's Law:

  • States that the total electric flux through a closed surface is proportional to the enclosed charge:
    $$ ext{Flux} = rac{Q{enc}}{ ext{ε0}}$$

  • Useful for calculating the electric field of symmetric charge distributions.

Chapter 23: Potential Difference and Electric Potential

• Electric Potential (V):

  • Defined as the electric potential energy per unit charge. Measured in Volts (V):
    $V = rac{U}{Q}$$$V = rac{U}{Q}$$

• Potential Difference (dV):

  • The work done per unit charge as a charge moves in an electric field:
    $dV = - ext{E} imes dl$$$dV = - ext{E} imes dl$$

Chapter 24: Capacitance

• Capacitance (C):

  • Defined as the ability of a system to store charge per unit voltage.

  • Unit: Farad (F)

  • $C = rac{Q}{V}$$$C = rac{Q}{V}$$

• Parallel Plate Capacitor:

  • Consists of two parallel plates with opposite charges, the electric field between them is uniform.

  • Energy stored in a capacitor is given by:
    $U = rac{1}{2}CV^2$$$U = rac{1}{2}CV^2$$

Chapter 25: Electric Current

• Electric Current (I):

  • Rate of flow of charge:
    $I = rac{dq}{dt}$$$I = rac{dq}{dt}$$

• Resistance (R):

  • Measure of the opposition to current flow:
    $R = rac{V}{I}$$$R = rac{V}{I}$$

• Kirchhoff's Rules:

  • Loop Rule: The sum of potential differences around any closed circuit must equal zero.

  • Junction Rule: The sum of currents entering a junction must equal the sum of currents leaving.

Chapter 26: Magnetism

• Magnetic Force (F_B):

  • Force on a moving charge in a magnetic field:
    $F_B = q(v imes B)$$$F_B = q(v imes B)$$

• Magnetic Field (B):

  • Defined directionally and has units of Teslas (T).

• Right-Hand Rule:

  • Used to determine the direction of the magnetic force.

Chapter 27: Ampere's Law

• Ampere’s Law:

  • Relates the integrated magnetic field around a closed loop to the electric current passing through the loop:
    $$ ext{∮} B ullet dL = μ0 I{enc}$$

• Biot-Savart Law:

  • Describes the magnetic field generated by a steady current; important for calculating fields in loops and coils.

Chapter 28: Induction and Inductance

• Faraday's Law of Electromagnetic Induction:

  • An electromotive force (emf) is induced in a circuit when the magnetic field through the circuit changes:
    $ext{emf} = - rac{d ext{Φ}_B}{dt}$$$ ext{emf} = - rac{d ext{Φ}_B}{dt}$$

• Inductance (L):

  • Defined as the ratio of induced emf to the rate of change of current. Unit: Henry (H).

Chapter 30: Maxwell's Equations

1. Gauss's Law for Electric Fields:
   $$

   dA = rac{Q{enc}}{ε0}
   $$

2. Gauss's Law for Magnetic Fields:
   $$

   ext{∮} B ullet da = 0 ext{ (no magnetic monopoles)}
   $$

3. Faraday's Law:
   $$

   ext{∮} E ullet dl = - rac{d}{dt} ext{Φ}_B
   $$

4. Ampere-Maxwell Law:
   $$ ext{∮} B ullet dl = μ0 imes I + μ0ε0 rac{dΦE}{dt}$$

Chapter 31: Wave Properties of Light

• Electromagnetic Waves:

  • Produced by oscillating electric and magnetic fields. Travel at the speed of light:
    $c = 3 imes 10^8 ext{ m/s}$$$c = 3 imes 10^8 ext{ m/s}$$

• Wave-Particle Duality:

  • Light exhibits both wave-like and particle-like properties.

Chapter 32: Reflection and Refraction

• Law of Reflection:

  • Angle of incidence equals the angle of reflection:
    $$θi = θr$$

• Snell's Law:

  • Describes the relationship between angle of incidence and refraction:
    $$n1 ext{ sin}θ1 = n2 ext{ sin}θ2$$

• Total Internal Reflection:

  • Occurs when light attempts to travel from a medium with a higher index of refraction to one with a lower index, beyond a critical angle, it reflects completely.

• Polarization of Light:

  • The orientation of light waves in a single direction, can be achieved using polarizing filters.