Biot-Savart law
Check the Biot-Savart law with a smartphone
Autor:
Título 4
Learning objectives :
This activity allows students to experimentally verify the relationship between the intensity of the electric current and the magnetic field produced. It develops the ability to establish a relationship between physical quantities and to deduce a law.
Concepts covered
Magnetic field; Electromagnetism; Biot-Savart law; Relationship of proportionality; Coils and solenoids
What students will do :
The student uses the FizziQ magnetometer to measure the magnetic field created by a coil carrying a current. By gradually varying the intensity of the current and recording the Y component of the magnetic field, the student draws a graph making it possible to determine the relationship between these two quantities and verifies the linearity predicted by the Biot-Savart law.
What is required :
Smartphone with the FizziQ application; A coil or solenoid; An adjustable direct current generator; Connection wires; A multimeter (optional) to measure precise intensity; FizziQ experience notebook
Scientific background :
The Biot-Savart law, established in 1820 by French physicists Jean-Baptiste Biot and Félix Savart, is one of the fundamental laws of electromagnetism. It describes how an electric current generates a magnetic field. For a coil or a solenoid, this law predicts that the magnetic field B at the center is directly proportional to the intensity of the current I passing through it, according to the relation B = µ₀nI, where µ₀ is the magnetic permeability of the vacuum (4π×10⁻⁷ T·m/A) and n the number of turns per unit length. The smartphone's magnetometer measures the magnetic field along three orthogonal axes with a sensitivity of approximately 0.1 µT. By aligning the Y axis of the magnetometer with the axis of the coil and calibrating the sensor to subtract the Earth's magnetic field, we can measure only the field created by the coil. The main experimental difficulties include: 1) Precise alignment of the smartphone relative to the coil; 2) Surrounding magnetic interference; 3) Heating of the coil for high currents which can slightly modify its resistance. By drawing the graph B = f(I), we should obtain a line whose slope corresponds to the factor µ₀n. Verification of this linearity confirms the validity of the Biot-Savart law for this configuration. This experiment provides an accessible introduction to electromagnetism and illustrates how an electric current can generate a magnetic field, a fundamental principle underlying many modern technologies such as electric motors, transformers or MRIs.