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 PermeabilityPhysical 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.
- 1Magnetic Field: Thumb (current) → Four fingers (field encircling wire)
- 2Lorentz Force: Four fingers (B) + Thumb (v) → Palm (F for positive charges)
- 3Wire Force: Four fingers (B) + Thumb (I) → Palm (F on wire)
- 4Negative charge (electron): Force direction opposite to palm
Categories:
How to Use the KalkuLab Magnetic Field Calculator
This calculator has 3 main modes. Follow the steps for your calculation:
- 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
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
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
Press Calculate
Click Calculate for instant results in SI units (Tesla for B, Newton for F).
- 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
A wire carries 500 A. What is B at 10 m distance? (μ₀ = 4π×10⁻⁷ H/m)
- 1.B = (μ₀ × I) / (2π × r)
- 2.B = (4π×10⁻⁷ × 500) / (2π × 10)
- 3.B = 10⁻⁵ T = 10 μT
The field at 10 m is 10 microtesla, comparable to Earth's magnetic field.
Example 2: Motor Wire Force
A 0.5 m wire in B = 0.8 T carries 4 A at 90°. What is the force?
- 1.F = B × I × L × sin(90°)
- 2.F = 0.8 × 4 × 0.5 × 1 = 1.6 N
1.6 N of force acts on the wire — this drives motor rotation.