Complete notes for Chapter 14 Electromagnetism. Covers Magnetic Field, Ampere's Law, Solenoid, Lorentz Force, CRO, Galvanometer, and Ammeter/Voltmeter conversion.
Oersted's Discovery: An electric current produces a magnetic field around it. The lines of force are circular concentric with the wire.
Right Hand Rule: If the wire is grasped in the fist of the right hand with the thumb pointing in the direction of current, the curled fingers indicate the direction of the magnetic field.
A current carrying conductor placed in a magnetic field experiences a force.
$$ F = I L B \sin \alpha $$
Where:
Vector Form: $$ \vec{F} = I (\vec{L} \times \vec{B}) $$
Direction: Determined by Right Hand Rule (rotate L to B).
Definition: The magnetic force on one meter length of a conductor carrying one ampere current placed at right angle to the magnetic field.
$$ B = \frac{F}{IL} $$
Unit - Tesla (T): Magnetic field is 1 Tesla if it exerts a force of 1 Newton on 1 meter conductor carrying 1 Ampere current perpendicular to field.
$$ 1 T = 1 N A^{-1} m^{-1} $$
Total number of magnetic lines of force passing through an area.
$$ \Phi_B = \vec{B} \cdot \vec{A} = BA \cos \theta $$
Where θ is the angle between B and Vector Area A (normal to surface).
Unit: Weber (Wb). $$ 1 Wb = 1 N m A^{-1} $$
The sum of quantities $$ \vec{B} \cdot \Delta \vec{L} $$ for all path elements equals $$ \mu_o $$ times the total current enclosed.
$$ \sum (\vec{B} \cdot \Delta \vec{L}) = \mu_o I $$
Permeability (μ₀): $$ 4\pi \times 10^{-7} Wb A^{-1} m^{-1} $$
Solenoid: A long tightly wound cylindrical coil of wire. Behaves like a bar magnet when current flows.
Magnetic Field (B): Using Ampere's Law on a rectangular loop partially inside the solenoid:
$$ B = \mu_o n I $$
Where n: Number of turns per unit length ($$ n = N/L $$).
Inside field is strong and uniform. Outside field is negligible.
A charge moving in a magnetic field experiences a force.
$$ \vec{F} = q (\vec{v} \times \vec{B}) $$
$$ F = q v B \sin \theta $$
Lorentz Force: The total force on a charge moving in a region with both Electric (E) and Magnetic (B) fields.
$$ \vec{F} = \vec{F}_e + \vec{F}_m = q\vec{E} + q(\vec{v} \times \vec{B}) $$
J.J. Thomson's experiment measuring charge-to-mass ratio.
Principle: Magnetic force provides centripetal force for circular motion.
$$ \frac{mv^2}{r} = e v B \implies \frac{e}{m} = \frac{v}{Br} $$
Velocity Selection: Using potential V to accelerate electron: $$ v = \sqrt{\frac{2Ve}{m}} $$
Substituting v:
$$ \frac{e}{m} = \frac{2V}{B^2 r^2} $$
A high-speed graph plotting device used to display voltage waveforms.
Display waveforms, measure voltage, frequency, and phase difference.
A coil placed in a magnetic field experiences a torque.
$$ \tau = N I A B \cos \alpha $$
Where:
If θ is angle between field and normal to area, then $$ \tau = N I A B \sin \theta $$.
A sensitive instrument used to detect small currents.
A current carrying coil placed in a magnetic field experiences a torque. $$ \tau_{deflecting} = N I A B $$ (assuming radial field, α=0).
Restoring torque by suspension: $$ \tau_{restoring} = C \theta $$
At equilibrium: $$ N I A B = C \theta \implies I = (\frac{C}{NAB}) \theta $$
Current Sensitivity: $$ \frac{\theta}{I} = \frac{NAB}{C} $$ (Radians per Ampere).
Converted by connecting a low resistance Shunt ($$ R_s $$) in parallel with galvanometer.
$$ R_s = \frac{I_g R_g}{I - I_g} $$
Ideally has zero resistance. Connected in series.
Converted by connecting a high resistance $$ R_h $$ in series with galvanometer.
$$ R_h = \frac{V}{I_g} - R_g $$
Ideally has infinite resistance. Connected in parallel.
An instrument to measure Current (Amperes), Voltage (Volts), and Resistance (Ohms).
Electronic instrument displaying values digitally. More accurate and easy to read.