Physics: Calculating Magnetic Forces Between Currents

Overview

• Focus on calculating magnetic forces between two currents.
• Two scenarios: Parallel Currents and Anti-parallel Currents.
• Application of right-hand rules to determine direction and magnitude of forces.

Key Concepts

Force Equation

• Magnetic Force Equation: ( F = IL \times B )
  • ( I ): Current
  • ( L ): Length of wire
  • ( B ): Magnetic field

Right-Hand Rules

• Right-Hand Rule #1: Determines direction of magnetic force.
  • Index finger: Direction of current.
  • Middle finger: Direction of magnetic field.
  • Thumb: Direction of magnetic force.
• Right-Hand Rule #2: Determines direction of magnetic field produced by a current.
  • Thumb: Direction of current.
  • Curl fingers: Direction of magnetic field (circumferential around the wire).

Case Study: Parallel Currents

Finding Magnetic Field and Force

1. Identify the magnetic field:
   • Use Right-Hand Rule #2 for the field produced by current ( I_1 ).
   • Field is circumferential and changes direction around the wire.
2. Calculate force on ( I_2 ):
   • Use Right-Hand Rule #1 to find the force direction.
   • Apply equation: ( F_2 = I_2 L B_1 \sin(\theta) )
     • ( B_1 = \frac{\mu_0 I_1}{2 \pi r} )
     • Calculate with ( \theta = 90^\circ ) (( \sin(90) = 1 )).

Force Magnitude

• Force per unit length: ( \frac{F}{L} = \frac{\mu_0 I_1 I_2}{2 \pi d} )
• Example calculation provided with numerical values.

Case Study: Anti-parallel Currents

Force Direction and Magnitude

• Reverse of Parallel Case:
  • Apply the same right-hand rules to find directions.
  • Forces act in opposite directions indicating repulsion.
• Same Magnitude as Parallel Currents:
  • Formula: ( \frac{F}{L} = \frac{\mu_0 I_1 I_2}{2 \pi d} )

Conclusions

• Parallel Currents: Attract each other.
• Anti-parallel Currents: Repel each other.
• Forces calculated using magnetic force equation and right-hand rules.

Important Notes

• Direction determined by right-hand rules crucial for solving problems.
• Magnitude depends on currents and distance between wires.
• Practical applications: Understanding interactions between parallel and anti-parallel currents can be critical in electrical engineering and physics.