Biot-Savart Law Calculator

The Biot-Savart law describes the magnetic field generated by a steady electric current. It states that the magnetic field B at any point is proportional to the current, the length of the current element, and inversely proportional to the square of the distance from the current element.

The magnetic field is calculated using the formula B = (μ₀/4π) × (Q × v × sin(θ))/r². Where μ₀ is the permeability of vacuum, Q is the point charge, v is velocity, θ is the angle between velocity and position vector, and r is the distance.

The permeability of vacuum (μ₀) is a fundamental physical constant equal to 4π × 10⁻⁷ H/m (henries per meter) or N/A² (newtons per ampere squared). It relates the magnetic field to the current that produces it.

The angle θ between the velocity vector and the position vector is crucial because it determines the sine component in the cross product. When θ = 90°, the magnetic field is maximum. When θ = 0° or 180°, the magnetic field is zero.

Magnetic field strength is measured in Tesla (T) in the SI system. One Tesla is equal to one weber per square meter (Wb/m²) or one newton per ampere-meter (N/(A·m)).

The magnetic field strength is inversely proportional to the square of the distance (1/r²). This means that doubling the distance reduces the magnetic field to one-fourth of its original value.

This calculator computes the magnetic field for a single current element or point charge. For multiple elements, you would need to calculate each contribution separately and then use vector addition to find the total field.

The Biot-Savart law can calculate magnetic fields for any current configuration, while Ampère's law is easier to use but only works for highly symmetric current distributions like infinite straight wires or circular loops.