Lecture on Magnetism

Basic Concepts of Magnetism

• Bar Magnets:
  • North poles repel each other
  • North pole and South pole attract each other
  • Each magnet has its own magnetic field moving from its North to South pole.

Magnetic Fields

• Created by moving electric charges.
• Example: A wire with electric current creates a magnetic field.
• The right-hand rule helps determine the direction of the magnetic field around a wire.
  • Thumb points in direction of current
  • Fingers curl in the direction of the magnetic field

Calculating Magnetic Field

• Equation: ( B = \frac{\mu_0 I}{2 \pi r} )
  • ( B ): Magnetic field (Tesla)
  • ( \mu_0 ): Permeability of free space, ( 4\pi \times 10^{-7} )
  • ( I ): Current (Amps)
  • ( r ): Distance from the wire (meters)
• Magnetic field strength increases with current and decreases with distance.

Magnetic Force

• A moving charge within a magnetic field experiences a force.
• Equation for a wire: ( F = ILB \sin \theta )
  • ( F ): Magnetic force
  • ( I ): Current
  • ( L ): Length of wire
  • ( B ): Magnetic field
  • ( \theta ): Angle between current and magnetic field
• Direction is perpendicular to both current and magnetic field (use right-hand rule).

Point Charge in Magnetic Field

• Equation: ( F = Bqv \sin \theta )
  • ( q ): Charge
  • ( v ): Velocity of the charge
• For a proton or electron moving perpendicular to magnetic field, use right-hand rule to determine force direction (opposite for electrons).

Circular Motion of Charges

• A charge moving perpendicular to a constant magnetic field moves in a circle.
• Centripetal force = Magnetic force: ( mv^2/r = Bqv )
• Radius of Path: ( r = \frac{mv}{Bq} )

Ampere’s Law

• Equation: ( \oint B \cdot dl = \mu_0 I )
  • Describes the relationship of current and the magnetic field it produces.
• Used to derive magnetic field inside a solenoid.

Solenoids

• Device with multiple loops of wire.
• Magnetic field inside is strong and uniform.
• Magnetic Field Equation: ( B = \mu_0 n I )
  • ( n ): Number of turns per meter
• Field is proportional to current and turns, inversely proportional to length.

Force Between Parallel Wires

• Two wires with current in the same direction attract each other; opposite directions repel.
• Force Equation: ( F = \frac{\mu_0 I_1 I_2 L}{2\pi r} )
  • ( L ): Length of the wire
  • ( r ): Distance between wires

Torque on a Current Loop

• A loop in a magnetic field experiences torque.
• Equation: ( \tau = n I A B \sin \theta )
  • ( \tau ): Torque
  • ( n ): Number of loops
  • ( A ): Area of the loop

Worked Problems

1. Calculate Magnetic Force: Use given equations to find magnetic fields and forces for varying configurations.
2. Determining Radius of Curvature: Apply centripetal force and magnetic force equivalence.
3. Solenoid Field Calculation: Use properties of solenoids to calculate internal magnetic fields.
4. Current Loop Torque: Calculate torque assuming maximum or known angles.

Summary

• Right-hand rule is crucial for determining directions of fields and forces.
• Magnetic fields have direct applications in electrical devices and physics.
• Understanding relationships between current, magnetic fields, and forces is fundamental in magnetism.