Lecture on Magnetism

Introduction to Magnetism

• Bar magnets have a North and South pole.
• Like poles repel (North-North, South-South), opposite poles attract (North-South).
• Magnetic fields travel from the North pole to the South pole.
• Magnetic fields cancel out when like poles are near one another.

Creation of Magnetic Fields

• Magnetic fields are created by moving electric charges.
• Example: Current flowing through a wire creates a magnetic field.

Right Hand Rule

• Thumb points in direction of current.
• Fingers curl in the direction of magnetic field around the wire.

Calculating Magnetic Field Strength

• Formula: ( B = \frac{\mu_0 I}{2\pi r} )
  • ( B ): Magnetic field strength in Tesla.
  • ( I ): Current in Amperes.
  • ( r ): Distance from wire.
  • ( \mu_0 ): Permeability of free space ( 4\pi \times 10^{-7} ) (Tesla \ times meter per Ampere).
• Magnetic field strength increases with current, decreases with distance.

Example Problems

1. Calculate magnetic field 2cm from a wire with 45A current.
   • Convert distance: ( 2cm = 0.02m )
   • Use formula to find ( B = 4.5 \times 10^{-4} ) Tesla.
2. Find distance where magnetic field is ( 8 \times 10^{-4} ) Tesla with 10A current.
   • Use rearranged formula to solve for ( r ).

Magnetic Forces and Moving Charges

• Moving charges experience magnetic forces.
• Formula for force on a wire: ( F = I L B \sin \theta )
  • ( F ): Magnetic force.
  • ( L ): Length of wire in the field.
  • ( \theta ): Angle between current and magnetic field (maximum force at (90^\circ)).

Direction of Magnetic Force

• Right hand rule is used to determine the direction.
• Thumb in current direction, fingers in magnetic field direction.

Calculation of Magnetic Force on Moving Charges

• Formula: ( F = B q v \sin \theta )
  • ( q ): Charge of particle.
  • ( v ): Velocity of particle.
  • Maximum when velocity and magnetic field are perpendicular.

Path of Charged Particles in Magnetic Fields

• Charged particles move in circular paths in magnetic fields.
• Use centripetal force equation to find the radius of curvature: ( r = \frac{mv}{Bq} )

Parallel Currents

• Wires with currents in the same direction attract; opposite directions repel.
• Force between wires: ( F = \frac{\mu_0 I_1 I_2 L}{2\pi r} )

Ampere’s Law

• Describes relationship between current and magnetic field in a closed loop.
• Integral of magnetic field over a closed loop is ( \mu_0 ) times the enclosed current.

Solenoids

• Solenoids create strong magnetic fields within.
• Formula for solenoid magnetic field: ( B = \mu_0 n I )
  • ( n ): Number of turns per unit length.

Torque on a Current Loop in a Magnetic Field

• A current loop in a magnetic field experiences torque.
• Torque formula: ( \tau = n I A B \sin \theta )
  • ( A ): Area of the loop.
• Maximum torque at ( \theta = 90^\circ ).

Example Problems and Applications

• Calculating force, magnetic fields, and torque in various configurations.
• Understanding the behavior of solenoids and current loops in magnetic fields.

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This summary covers the key concepts and equations discussed in the lecture on magnetism, including the creation and calculation of magnetic fields and forces, the behavior of charges and wires in magnetic fields, and the application of Ampere’s Law and torque calculations for loops and solenoids. Use these notes to study and refer back to important formulas and principles.