Electricity and Magnetism — NDA Physics

Formulas (3)

• Coulomb's law — force between two charges · Coulomb's law
  $$F = \dfrac{1}{4\pi\varepsilon_0}\,\dfrac{q_1 q_2}{r^2} = k\,\dfrac{q_1 q_2}{r^2}$$
• Electric field and field lines · Electric field (definition)
  $$E = \dfrac{F}{q}$$
• Electric potential and potential difference · Potential difference / work
  $$V = \dfrac{W}{q} \quad\Longleftrightarrow\quad W = qV$$

Reference tables (1)

Watch out for (7)

• "Charges can be created and destroyed" is the WRONG option
  → Electric charge and its three properties
• Only electrons move — never protons
  → How objects get charged — friction and induction
• "Positive force" = repulsion = like charges
  → Coulomb's law — force between two charges
• Outward AND perpendicular — both words matter
  → Electric field and field lines
• Divide work by charge — don't multiply
  → Electric potential and potential difference
• Field is zero INSIDE THE METAL (a<r<b), not everywhere
  → Conductors in electrostatics — field-free interior
• A sharp tip ENHANCES the field — it doesn't reduce it
  → Sharp points, corona discharge and lightning protection

Formulas (2)

• Electric current as rate of flow of charge · Current and charge
  $$I = \dfrac{Q}{t} \quad\Longleftrightarrow\quad Q = I\,t$$
• Ohm's law — V = IR · Ohm's law
  $$V = I\,R$$

Reference tables (1)

Watch out for (5)

• Convert minutes to seconds first
  → Electric current as rate of flow of charge
• Free electrons, not 'both bound and free'
  → What carries current in a metal — free electrons
• Ohm's law is NOT universal
  → Ohm's law — V = IR
• A rheostat is ohmic; a diode is not
  → Ohmic vs non-ohmic conductors
• Reverses every 1/100 s, not 1/50 s
  → Alternating current vs direct current

Formulas (2)

• Resistance and what controls it · Resistance of a uniform wire
  $$R = \rho\,\dfrac{L}{A}$$
• Stretching and cutting a wire · Stretched wire (constant volume)
  $$R' = k^2 R \quad\text{when length}\to kL,\ \text{area}\to A/k$$

Watch out for (3)

• Current does not affect resistance
  → Resistance and what controls it
• Stretching changes R, not ρ
  → Resistivity — the material's own property
• Stretching is R ∝ L², not R ∝ L
  → Stretching and cutting a wire

Formulas (3)

• Resistors in series · Series equivalent
  $$R_\text{series} = R_1 + R_2 + \cdots + R_n$$
• Resistors in parallel · Parallel equivalent
  $$\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots \qquad (\text{two: } R = \tfrac{R_1R_2}{R_1+R_2})$$
• Cutting a wire and reconnecting it · Cut into n, reconnect in parallel
  $$R_\text{final} = \dfrac{R}{n^2}$$

Watch out for (5)

• Series = same current, voltages add
  → Resistors in series
• Parallel value is SMALLER than the smallest branch
  → Resistors in parallel
• Collapse innermost first — don't add everything blindly
  → Reducing mixed series-parallel networks
• Cut + parallel = R/n², not R/n
  → Cutting a wire and reconnecting it
• Minimum ≠ fewest resistors
  → Minimum and maximum resistance

Formulas (4)

• Electrical power — three equivalent forms · Electrical power
  $$P = VI = I^2 R = \dfrac{V^2}{R}$$
• Power rating and running at the wrong voltage · Power vs voltage at fixed R
  $$P = \dfrac{V^2}{R}, \quad R = \dfrac{V_0^2}{P_0} \;\Rightarrow\; \dfrac{P}{P_0} = \left(\dfrac{V}{V_0}\right)^2$$
• Electrical energy and the cost of running appliances · Energy and cost
  $$E\,(\text{kWh}) = P\,(\text{kW}) \times t\,(\text{h}), \qquad \text{Cost} = E \times \text{rate}$$
• Joule heating — current heats a resistor · Joule heating
  $$H = I^2 R\,t = V I t = \dfrac{V^2}{R}\,t$$

Watch out for (5)

• I²R is power; IR² and I²/R are not
  → Electrical power — three equivalent forms
• Power scales as V², not V
  → Power rating and running at the wrong voltage
• Keep power in kW and time in hours
  → Electrical energy and the cost of running appliances
• Heat depends on all of V, I, and t
  → Joule heating — current heats a resistor
• Same VOLTAGE → use V²/R; don't reach for I²R
  → Heat dissipation in series vs parallel

Formulas (2)

• EMF, internal resistance and terminal voltage · Terminal voltage and circuit current
  $$V = \varepsilon - I r, \qquad I = \dfrac{\varepsilon}{R + r}$$
• Kirchhoff's two laws · Kirchhoff's laws
  $$\sum_\text{junction} I = 0, \qquad \sum_\text{loop} (\varepsilon - IR) = 0$$

Watch out for (3)

• Terminal voltage drops as current rises
  → EMF, internal resistance and terminal voltage
• Loop rule = energy; junction rule = charge
  → Kirchhoff's two laws
• Parallel bulbs each get full voltage — series bulbs split it
  → Combining cells and bulb brightness

Formulas (3)

• Magnetic field of a current-carrying straight wire · Field of a straight wire
  $$B = \dfrac{\mu_0 I}{2\pi r}$$
• Magnetic field of a solenoid · Field inside a solenoid
  $$B = \mu_0 n I$$
• Magnetic field at the centre of a circular coil · Field at centre of a coil
  $$B = \dfrac{\mu_0 N I}{2R}$$

Reference tables (1)

Watch out for (6)

• Field lines are CLOSED and exist INSIDE the magnet
  → Magnets and magnetic field lines
• Magnetic EQUATOR, not magnetic meridian
  → The Earth's magnetic field
• Stainless steel is (usually) magnetic; aluminium is only weakly so
  → Magnetic materials — what a magnet attracts
• Depends on current and distance — not on the wire's radius
  → Magnetic field of a current-carrying straight wire
• Field depends on turns-per-length and current, not diameter
  → Magnetic field of a solenoid
• Combine the factors: N up AND R down both raise B
  → Magnetic field at the centre of a circular coil

Formulas (2)

• Force on a charge moving in a magnetic field · Magnetic force on a moving charge
  $$F = qvB\sin\theta$$
• Force on a current-carrying conductor — Fleming's left-hand rule · Force on a current-carrying conductor
  $$F = B I L$$

Watch out for (3)

• No force when motion is ALONG (or against) the field
  → Force on a charge moving in a magnetic field
• LEFT hand for force (motor), not right
  → Force on a current-carrying conductor — Fleming's left-hand rule
• Right hand → induced current (generator)
  → Induced current — Fleming's right-hand rule

Formulas (1)

• Transformers — changing AC voltage · Transformer turns ratio
  $$\dfrac{V_s}{V_p} = \dfrac{N_s}{N_p}$$

Reference tables (4)

Watch out for (5)

• Nichrome heats, tungsten lights — don't swap them
  → Heating elements and bulb filaments
• Fuse = LOW melting point (and conducting)
  → Fuses, earthing and household wiring
• Generator produces current; motor consumes it
  → Generators, motors and the AC/DC distinction
• Transformers change VOLTAGE, not power — and need AC
  → Transformers — changing AC voltage
• Voltmeter HIGH resistance, ammeter LOW — the common swap
  → Meters, conductors and insulators