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What is a Magnetic Field?

A magnetic field is the region around a magnet or a current-carrying wire where magnetic force can be felt. This concept is a fundamental part of electromagnetism that explains natural phenomena such as Earth's magnetism to modern technological applications like electric motors, generators, and MRI (Magnetic Resonance Imaging). Kalkulab's Magnetic Field Calculator is specifically designed to help high school students (grade 12), physics students, and technicians understand and calculate quantities related to magnetic fields. This tool covers three main calculations: (1) Magnetic field around a straight current-carrying wire using Ampere's law, (2) Lorentz force on moving charges, and (3) Magnetic force on current-carrying wires.

Magnetic Field & Lorentz Force Formula

B = (μ₀ × I) / (2π × r)Formula: F = q × v × B × sin(θ); F = B × I × L × sin(θ)

Variables:

  • BMagnetic Field (Tesla)
    Strength of magnetic field at a point(e.g.: 0.0001 T)
    💡 Magnetic field around a wire
  • μ₀Vacuum Permeability
    Physical constant = 4π × 10⁻⁷ H/m(e.g.: 1.2566×10⁻⁶ H/m)
    💡 Constant in magnetic field formula
  • IElectric Current (Amperes)
    Amount of current flowing in the wire(e.g.: 5 A)
    💡 Current in a conducting wire
  • rDistance (meters)
    Distance from wire to observation point(e.g.: 0.1 m)
    💡 Field measurement from wire
  • FForce (Newtons)
    Lorentz force or force on wire(e.g.: 1.6×10⁻¹⁹ N)
    💡 Force on electron or wire
  • qElectric Charge (Coulombs)
    Amount of moving electric charge(e.g.: 1.6×10⁻¹⁹ C)
    💡 Charge of electron or proton
  • vVelocity (m/s)
    Velocity of moving charge(e.g.: 10⁶ m/s)
    💡 Electron velocity in cathode ray tube
  • LWire Length (meters)
    Length of wire in the magnetic field(e.g.: 0.5 m)
    💡 Wire length in an electric motor
  • θAngle (degrees)
    Angle between velocity/current direction and field(e.g.: 90°)
    💡 Perpendicular angle produces maximum force

Right Hand Rule

The right hand rule is used to determine the direction of magnetic field, Lorentz force, or electric current. (1) Thumb direction = current (I) or velocity (v) direction, (2) Four fingers direction = magnetic field (B) direction, (3) Palm direction = force (F) direction for positive charges.

  1. 1Magnetic Field: Thumb (current) → Four fingers (field encircling wire)
  2. 2Lorentz Force: Four fingers (B) + Thumb (v) → Palm (F for positive charges)
  3. 3Wire Force: Four fingers (B) + Thumb (I) → Palm (F on wire)
  4. 4Negative charge (electron): Force direction opposite to palm

Categories:

Straight Wire FieldB = μ₀I/(2πr)
Lorentz ForceF = qvB sin(θ)
Wire ForceF = BIL sin(θ)
Earth's FieldEarth ≈ 25-65 μT

How to Use the KalkuLab Magnetic Field Calculator

This calculator has 3 main modes. Follow the steps for your calculation:

  1. 1

    Select Calculation Mode

    Choose: (1) Magnetic field around a straight current-carrying wire, (2) Lorentz force on a moving charge, or (3) Force on a current-carrying wire in a magnetic field.

  2. 2

    Enter Parameter Values

    Enter known values: current (I), distance (r), charge (q), velocity (v), length (L), or angle (θ). Use SI units (A, m, C, m/s, T).

  3. 3

    Set Angle (If Needed)

    For Lorentz force or wire force, enter the angle between velocity/current and the magnetic field. 90° gives maximum force (sin 90° = 1).

  4. 4

    Press Calculate

    Click Calculate for instant results in SI units (Tesla for B, Newton for F).

  5. 5

    Analyze Force Direction (Optional)

    Use the right-hand rule to determine force or field direction — important for vector analysis.

💡 Tip:

  • 1 Tesla = 10,000 Gauss. Earth's field is about 25–65 μT
  • For negative charges (electrons), Lorentz force direction is opposite the right-hand rule
  • At 0° or 180°, force is zero (sin 0° = sin 180° = 0)
  • Magnetic field is proportional to current and inversely proportional to distance
  • Use scientific notation for very small/large numbers

Examples

Example 1: Field Around a Power Line

Problem:

A wire carries 500 A. What is B at 10 m distance? (μ₀ = 4π×10⁻⁷ H/m)

Solution:
  1. 1.B = (μ₀ × I) / (2π × r)
  2. 2.B = (4π×10⁻⁷ × 500) / (2π × 10)
  3. 3.B = 10⁻⁵ T = 10 μT
Result:10 μT

The field at 10 m is 10 microtesla, comparable to Earth's magnetic field.

Example 2: Motor Wire Force

Problem:

A 0.5 m wire in B = 0.8 T carries 4 A at 90°. What is the force?

Solution:
  1. 1.F = B × I × L × sin(90°)
  2. 2.F = 0.8 × 4 × 0.5 × 1 = 1.6 N
Result:1.6 N

1.6 N of force acts on the wire — this drives motor rotation.

Frequently Asked Questions

What is a magnetic field?
A magnetic field is the region around a magnet or current-carrying wire where magnetic force can be detected. It is measured in Tesla (T). Earth's field is about 25–65 μT.
What is the Lorentz force?
The Lorentz force on a charge in a magnetic field: F = qvB sin(θ). Applications include CRT displays, mass spectrometers, and electric motors.
How do you use the right-hand rule?
Thumb = velocity (for positive charge), fingers = magnetic field direction, palm = force direction. Reverse for negative charges.
Is the KalkuLab Magnetic Field Calculator free?
Yes, completely free on KalkuLab.

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References