Complete notes for Chapter 15 Electromagnetic Induction. Covers Induced EMF, Motional EMF, Faraday's Law, Lenz's Law, Mutual and Self Induction, Generator, Motor, and Transformers.
Definition: If the magnetic flux through a circuit changes, an emf and a current are induced in the circuit. This phenomenon is called electromagnetic induction.
The emf induced by the motion of a conductor across a magnetic field.
$$ \varepsilon = -vBL \sin \theta $$
Where:
Mechanism: Magnetic force $$ F_m = qvB $$ acts on charges in the rod, accumulating them at ends, creating an electric field E. Equilibrium is reached when $$ qE = qvB $$.
The average emf induced in a conducting coil of N loops is equal to the negative of time rate of change of magnetic flux through the coil.
$$ \varepsilon = -N \frac{\Delta \Phi}{\Delta t} $$
Negative sign indicates the direction of induced emf opposes the change in flux.
Statement: The direction of induced current is always such as to oppose the change which causes the current.
Conservation of Energy: The mechanical work done to move the magnet/conductor against the opposing magnetic force is converted into electrical energy (induced current).
The phenomenon in which a changing current in one coil induces an emf in another coil.
$$ \varepsilon_s = -M \frac{\Delta I_p}{\Delta t} $$
Where M is Mutual Inductance.
Unit of M: Henry (H). 1 H = 1 V s A^-1.
The phenomenon in which a changing current in a coil induces an emf in itself.
$$ \varepsilon = -L \frac{\Delta I}{\Delta t} $$
Where L is Self Inductance.
Known as Back EMF because it opposes the change in current according to Lenz's law.
Energy is stored in the magnetic field of an inductor.
$$ U_m = \frac{1}{2} L I^2 $$
Energy Density: Energy per unit volume.
$$ u = \frac{B^2}{2 \mu_o} $$
A device that converts mechanical energy into electrical energy using electromagnetic induction.
Principle: Coil rotated in magnetic field induces emf.
$$ \varepsilon = N \omega A B \sin (\omega t) $$
Produces Alternating Current (AC).
DC Generator: Uses split-ring commutator to produce unidirectional current.
DC Motor: Converts electrical energy into mechanical energy. Principle is torque on current carrying coil in magnetic field.
Back EMF: Induced emf in motor opposes applied voltage. $$ V = \varepsilon_{back} + I R $$
A device to change AC voltage levels using mutual induction.
Turns Ratio: $$ \frac{V_s}{V_p} = \frac{N_s}{N_p} $$
Ideal Power: $$ P_{in} = P_{out} \implies V_p I_p = V_s I_s $$
Step-Up: $$ N_s > N_p \implies V_s > V_p $$
Step-Down: $$ N_s < N_p \implies V_s < V_p $$
Power Losses: Eddy currents (minimized by laminating core), Hysteresis (soft iron core).