Lecture Notes: Magnetic Forces on Current Carriers and Conductors

Key Concepts

• Magnetic Force Between Wires:
  • Parallel currents (same direction): Attractive force.
  • Anti-parallel currents (opposite directions): Repulsive force.
• Right-Hand Rule (RHR):
  • Thumb in direction of current; fingers curl in direction of magnetic field lines.
  • Magnetic field vector is always tangent to concentric circles around a wire.

Magnetic Field Calculation

• Straight Long Wire:
  • Magnetic Field, (B = \frac{\mu_0 I}{2\pi r}), where:
    • (\mu_0) is the magnetic constant (4\pi \times 10^{-7}\ \text{T} \cdot \text{m/A}).
    • (I) is current (in Amps).
    • (r) is the radius (distance from wire).
• Ring:
  • Magnetic field at center, (B_{center} = \frac{\mu_0 I}{2R}).
  • For (N) loops, (B = N \frac{\mu_0 I}{2R})._

Solenoids

• Magnetic Field Inside Solenoid:
  • (B_{inside} = n \mu_0 I), where (n = \frac{N}{L}) (turns per unit length).
  • Magnetic field outside solenoid: (B = 0)._

Magnetic Force on Wire

• Force on wire in a magnetic field: (F = ILB).
  • (I) is current.
  • (L) is length of wire.
  • (B) is magnetic field.
  • Force is perpendicular to wire and magnetic field.

Magnetic Force on Charged Particle

• Perpendicular Velocity:
  • Force, (F = QvB), where (Q) is charge, (v) is velocity, (B) is magnetic field.
• Angle to Magnetic Field:
  • Force, (F = QvB \sin(\theta)).

Cross Product for Force Calculation

• Force as Vector:
  • (F = Q(\mathbf{v} \times \mathbf{B})) or (F = I(\mathbf{L} \times \mathbf{B})), apply RHR.

Example Calculations

• Force on Wire Segment:
  • Determine (B), use (B = \mu_0 \frac{I}{2\pi r}) for one wire affecting another.
• Force Due to Solenoid on Loop:
  • Use (F = ILB \sin(\phi)).
  • Consider equilibrium for tension calculations with forces (T + F_B = mg).

Additional Examples

• Parallel Wires:
  • Calculate forces between wires using derived magnetic fields from currents.
• Net Magnetic Field at a Point:
  • Calculate contributions from multiple sources and sum their vectors.
  • Use RHR to determine direction.

Summary

• Use RHR extensively for determining directions of fields and forces.
• Understand formulas for different configurations of wires and current flows.
• Solve examples by applying formulas and calculating net results.