Magnetic Force on a Current Carrying Wire Calculator

Electromagnetism Physics

Calculate the magnetic force acting on a current-carrying wire placed in a magnetic field using Lorentz force law. Essential for electromagnetism studies, electrical engineering, and physics calculations.

Examples

Click on any example to load it into the calculator.

Laboratory Experiment

Laboratory Experiment

Typical laboratory setup with 2A current, 30cm wire length, and perpendicular magnetic field.

Current: 2 A

Wire Length: 0.3 m

Distance: 0.05 m

Angle: 90 °

Relative Permeability: 1

Electric Motor Coil

Electric Motor Coil

Electric motor coil with 10A current, 20cm length, and 45° angle to magnetic field.

Current: 10 A

Wire Length: 0.2 m

Distance: 0.02 m

Angle: 45 °

Relative Permeability: 1

Transformer Winding

Transformer Winding

Transformer winding with 5A current, 1m length, and parallel orientation.

Current: 5 A

Wire Length: 1 m

Distance: 0.1 m

Angle: 0 °

Relative Permeability: 1000

Power Line in Magnetic Field

Power Line in Magnetic Field

High voltage power line with 1000A current, 100m length, and 30° angle.

Current: 1000 A

Wire Length: 100 m

Distance: 50 m

Angle: 30 °

Relative Permeability: 1

Other Titles
Understanding Magnetic Force on a Current Carrying Wire: A Comprehensive Guide
Explore the fundamental principles of electromagnetism, Lorentz force law, and how magnetic fields interact with current-carrying conductors.

What is Magnetic Force on a Current Carrying Wire?

  • The Fundamental Concept
  • Lorentz Force Law
  • Right-Hand Rule for Direction
When a current-carrying wire is placed in a magnetic field, it experiences a force known as the magnetic force or Lorentz force. This is one of the fundamental principles of electromagnetism, combining the effects of electric current and magnetic fields.
The Physics Behind Magnetic Force
The magnetic force on a current-carrying wire is given by the Lorentz force law: F = I × L × B × sin(θ), where F is the magnetic force, I is the current, L is the length of the wire in the magnetic field, B is the magnetic field strength, and θ is the angle between the wire and the magnetic field direction.
Magnetic Field Generation
The magnetic field around a straight current-carrying wire is calculated using Ampere's law: B = (μ₀ × μᵣ × I) / (2π × r), where μ₀ is the permeability of free space (4π × 10⁻⁷ T⋅m/A), μᵣ is the relative permeability, I is the current, and r is the distance from the wire.

Key Concepts:

  • Magnetic force is maximum when wire is perpendicular to field
  • Force is zero when wire is parallel to field
  • Force direction follows right-hand rule

Step-by-Step Guide to Using the Magnetic Force Calculator

  • Understanding Your Inputs
  • Choosing the Right Parameters
  • Interpreting the Results
This calculator helps you determine the magnetic force acting on a current-carrying wire placed in a magnetic field. Follow these steps to get accurate results for your specific application.
1. Determine the Current
Measure or obtain the electric current flowing through the wire. This is typically measured in Amperes (A). Common values range from milliamperes (mA) for small electronics to thousands of amperes for power transmission lines.
2. Measure the Wire Length
Determine the length of the wire segment that is exposed to the magnetic field. This should be measured in meters (m). Only the portion of the wire in the magnetic field contributes to the force calculation.
3. Calculate Distance and Field
The distance from the wire determines the magnetic field strength. The field strength decreases with distance according to Ampere's law. The relative permeability depends on the surrounding medium.
4. Determine the Angle
The angle between the wire direction and the magnetic field direction is crucial. Use 90° for perpendicular orientation (maximum force), 0° for parallel orientation (zero force), or any angle between 0° and 180°.
5. Analyze Your Results
The calculator provides the magnetic force in Newtons (N), the magnetic field strength in Tesla (T), and the force direction. The force direction follows the right-hand rule for cross products.

Common Applications:

  • Electric motors and generators
  • Electromagnetic actuators
  • Physics education and laboratory experiments

Real-World Applications of Magnetic Force Calculations

  • Electric Motors
  • Electromagnetic Actuators
  • Scientific Research
Understanding magnetic forces on current-carrying wires is essential for many modern technologies and scientific applications.
Electric Motors and Generators
Electric motors work by placing current-carrying coils in magnetic fields. The magnetic force causes the coils to rotate, converting electrical energy to mechanical energy. Generators work in reverse, converting mechanical energy to electrical energy.
Electromagnetic Actuators
Electromagnetic actuators use magnetic forces to create linear or rotational motion. These are used in valves, switches, relays, and other control systems where precise mechanical movement is required.
Magnetic Levitation
Magnetic levitation systems use carefully controlled magnetic forces to suspend objects without physical contact. This technology is used in high-speed trains, precision instruments, and research applications.

Industrial Applications:

  • Automotive electric motors
  • Industrial automation systems
  • Medical imaging equipment

Common Misconceptions and Correct Methods

  • Force Direction Confusion
  • Field Strength Assumptions
  • Angle Considerations
Several common misconceptions can lead to incorrect calculations and understanding of magnetic forces on current-carrying wires.
Force Direction and Right-Hand Rule
A common misconception is that the force always points in the direction of the magnetic field. In reality, the force is perpendicular to both the current direction and the magnetic field direction, following the right-hand rule for cross products.
Magnetic Field Strength Assumptions
Many people assume that the magnetic field strength is constant or uniform. In reality, the field strength varies with distance from the wire and depends on the medium's permeability. The field strength decreases as 1/r for a straight wire.
Angle Dependence
The magnetic force depends on the sine of the angle between the wire and the magnetic field. This means the force is maximum at 90° and zero at 0° or 180°. Many calculations incorrectly assume maximum force regardless of orientation.

Common Errors:

  • Ignoring angle dependence in force calculations
  • Assuming uniform magnetic field strength
  • Incorrect force direction determination

Mathematical Derivation and Examples

  • Lorentz Force Law Derivation
  • Magnetic Field Calculation
  • Practical Examples
The mathematical foundation of magnetic forces on current-carrying wires combines several fundamental principles of electromagnetism.
Lorentz Force Law Derivation
The Lorentz force law for a current-carrying wire can be derived from the force on individual moving charges: F = qvB sin(θ). For a wire with current I, length L, and n charges per unit volume, the total force becomes F = I × L × B × sin(θ).
Magnetic Field from Current-Carrying Wire
Ampere's law states that the line integral of the magnetic field around a closed loop equals μ₀ times the current enclosed. For a long straight wire, this gives B = (μ₀ × μᵣ × I) / (2π × r), where r is the distance from the wire.
Combined Force Calculation
Combining the Lorentz force law with the magnetic field calculation gives: F = I × L × [(μ₀ × μᵣ × I) / (2π × r)] × sin(θ). This can be simplified to F = (μ₀ × μᵣ × I² × L × sin(θ)) / (2π × r).

Mathematical Examples:

  • Force calculation for perpendicular wire
  • Field strength variation with distance
  • Angle dependence in force magnitude