Magnetic Fields & Lorentz Force Lab

Investigate how electric currents create magnetic fields and how those fields exert forces on moving charges. Explore the Biot-Savart law for wires, loops, and solenoids, then study the Lorentz force, cyclotron motion, and the interaction between parallel current-carrying wires.

Guided Experiment: B-Field vs Distance

How does the magnetic field strength from a long straight wire depend on distance? Predict the relationship between B and r.

Write your hypothesis in the Lab Report panel, then click Next.

Wire Cross-Section

Probe (r)r = 0.020 mI = 5 A

Controls

5 A
0.02 m

B-Field Result

Magnetic field B5.00e-5 T
DirectionConcentric circles around the wire (right-hand rule)

Data Table

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#SourceI(A)r(m)B(T)F(N)
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Reference Guide

Biot-Savart Law

A current-carrying wire produces a magnetic field that circles around it. The field strength at distance r from an infinite wire is given by

B=μ0I2πrB = \frac{\mu_0 I}{2\pi r}

For a circular loop of radius R, the on-axis field at distance x from the center is

B=μ0IR22(R2+x2)3/2B = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}

A solenoid with n turns per meter produces a uniform internal field B = μ₀nI.

Lorentz Force

A charged particle moving through a magnetic field experiences a force perpendicular to both its velocity and the field.

F⃗=qv⃗×B⃗  ⟹  F=qvBsin⁡θ\vec{F} = q\vec{v} \times \vec{B} \implies F = qvB\sin\theta

The force is maximum when the velocity is perpendicular to the field (θ = 90°) and zero when parallel (θ = 0°). The force never does work because it is always perpendicular to the velocity.

Cyclotron Motion

When a charged particle moves perpendicular to a uniform magnetic field, the Lorentz force acts as a centripetal force, producing circular motion.

r=mvqB,f=qB2πmr = \frac{mv}{qB}, \quad f = \frac{qB}{2\pi m}

The cyclotron radius depends on the particle's momentum (mv). The cyclotron frequency depends only on the charge-to-mass ratio and the field strength, not on the speed.

Parallel Wire Forces

Two parallel current-carrying wires exert forces on each other through their magnetic fields. The force per unit length is

FL=μ0I1I22πd\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}

Currents flowing in the same direction attract. Currents in opposite directions repel. This relationship was historically used to define the SI unit of current (the ampere).