Magnetic Force Calculator

Category: Physics
- November 06, 2025
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Calculate the magnetic force between two electrical currents or between a current and a moving charge. This calculator supports various configurations and provides step-by-step explanations.

Select Calculation Type

Wire Configuration

Advanced Options

About Magnetic Force

Magnetic forces arise from the interaction between moving charges or currents and magnetic fields. These forces are fundamental in electromagnetism and have numerous applications in technology.

Force Between Parallel Currents

When two current-carrying wires are placed parallel to each other, they exert a magnetic force on each other. This force is described by:

  • Force per unit length: F/L = (μ₀ × I₁ × I₂) / (2π × r)
  • Parallel currents in the same direction attract each other
  • Parallel currents in opposite directions repel each other
Lorentz Force on Moving Charges

A charged particle moving through a magnetic field experiences a force known as the Lorentz force:

  • Force: F = q × v × B × sin(θ)
  • The direction of the force is perpendicular to both the velocity and the magnetic field
  • The force is maximum when the velocity is perpendicular to the field (θ = 90°)
  • The force is zero when the velocity is parallel to the field (θ = 0° or 180°)
Magnetic Field of a Straight Wire

A straight current-carrying wire creates a magnetic field around it:

  • Field strength: B = (μ₀ × I) / (2π × r)
  • The field lines form concentric circles around the wire
  • The field strength decreases inversely with distance from the wire
Magnetic Field of a Solenoid

A solenoid is a coil of wire that creates a nearly uniform magnetic field inside it:

  • Field inside (ideal solenoid): B = μ₀ × n × I
  • Where n is the number of turns per unit length (N/L)
  • The field inside a long solenoid is nearly uniform and parallel to the axis
  • The field outside an ideal solenoid is approximately zero
Applications of Magnetic Forces

Magnetic forces have numerous practical applications:

  • Electric Motors: Convert electrical energy to mechanical energy
  • Generators: Convert mechanical energy to electrical energy
  • Electromagnets: Create controllable magnetic fields
  • Particle Accelerators: Use magnetic fields to guide charged particles
  • MRI Machines: Use strong magnetic fields for medical imaging
  • Magnetic Levitation: Used in maglev trains and other applications

Understanding the Magnetic Force Calculator

The Magnetic Force Calculator helps you find the magnetic force between two electrical currents or between a current and a moving charge. It's designed to cater to various configurations, making it a versatile tool for students and professionals alike. Whether you need to calculate the force between parallel wires or the force on a charge in a magnetic field, this calculator has you covered.

How to Choose Your Calculation Type

You can select between two primary calculation types: the force between two currents or the force on a moving charge in a magnetic field. This flexibility allows users to focus on the specific scenario they are working on. The options include:

  • Force Between Two Currents
  • Force on Moving Charge in Magnetic Field

Inputting Your Values for Currents

When calculating the magnetic force between two currents, you’ll need to input values such as the current in each wire, the distance between them, and the length of the wires. You can choose the wire configuration, whether they are parallel, perpendicular, or at an angle. This ensures that your calculations reflect the real-world setup accurately.

Calculating Force on a Moving Charge

If you're focused on the force acting on a moving charge, you'll be required to enter details regarding the magnetic field's configuration. This includes the type of field source, such as a straight wire or solenoid, and the distance from the charge to the field. Additionally, you will need to provide the charge's magnitude and its velocity, making the calculations comprehensive and precise.

Advanced Options for Precision

The calculator also includes advanced options that allow for further customisation. Users can adjust the number of decimal places for the output and choose to display visualisation and calculation steps. These features enhance understanding and cater to individual preferences, whether you're a learner or an expert.

Visualising the Results

Once you've entered your values, the calculator will provide you with detailed results. It includes the magnetic force value, the magnetic field strength, and even allows for visualisation of the magnetic field setup. This visual representation helps in grasping the concept of magnetic forces more effectively.

Learning About Magnetic Forces

Along with the calculations, the Magnetic Force Calculator offers a section on the theory behind magnetic forces. You'll learn about the fundamental principles of electromagnetism, including:

  • Force between parallel currents
  • Lorentz force on moving charges
  • Magnetic fields of straight wires and solenoids

Practical Applications of the Calculator

Using the Magnetic Force Calculator can be beneficial in various practical fields. Whether you're working in electrical engineering, Physics, or even in designing electric motors and generators, this tool provides essential insights into how magnetic forces operate in real-life scenarios. From understanding basic concepts to applying them in advanced projects, this calculator is a valuable resource.