Lecture Notes on Electricity and Magnetism

Key Concepts

Magnetic Field and Magnetic Force
- Direction of magnetic force
- Magnetic compass needle deflection when current passes through a wire
- Magnetic field forms loops, unlike electric field
- Principle of superposition applies to magnetic fields
Magnetic Force Calculation
- Formula: ( F_m = q \cdot (\vec{v} \times \vec{B}) )
- Magnetic force depends on the angle (( \theta )) between velocity and magnetic field
  - ( \theta = 0^\circ \rightarrow F_m = 0 )
  - ( \theta = 90^\circ \rightarrow F_m = qvb )
  - ( \theta = 180^\circ \rightarrow F_m = 0 )
Magnetic Forces on Moving Charges
- Force leads charges to move in specific patterns
- Magnetic field unit: Tesla (T)
- Dimensions of T: ( 10^{-4} ) Tesla
Direction of Magnetic Field and Force
- Right-hand rule for linear conductors
- Thumb = current direction, fingers = magnetic field
Lorentz Force
- Magnetic force = ( q(\vec{E} + \vec{v} \times \vec{B}) )
- Direction of Lorentz force depends on the charge sign

Continuous Charge Distribution
- Current density formula: ( J = nqv_d )
- Magnetic force formula for a conductor: ( F_m = ILB \sin \theta )
- Centripetal force in a magnetic field
Helical Motion
- Radius of helix: ( R = \frac{mv}{qB} )
- Time period: ( T = \frac{2\pi m}{qB} )
- Pitch: ( V_{\parallel} T )
- Frequency of rotation: ( \omega = \frac{qB}{m} )

Motion in Combined Fields
- Electric field (E) and magnetic field (B) should be opposite
- Formula: ( F = q(E - vB) )
- Force is zero if ( E - vB = 0 )
- Example: Thomson experiment