Formulas to Remember
Here are some more formulas related to the Biot-Savart law and the magnetic fields produced by current-carrying wires:
Magnetic field of a straight wire: The magnetic field at a point (P) a distance (r) from a long, straight wire carrying a current (I) is given by:
where ((\mu_0)) is the permeability of free space.
Magnetic field of a circular loop: The magnetic field at the center of a circular loop of radius (R) carrying a current (I) is given by:
Magnetic field of a solenoid (long, thin coil): The magnetic field inside a solenoid is given by:
Magnetic force between two parallel wires: The force between two long, parallel wires carrying currents (I_1) and (I_2) separated by a distance (d) is given by:
Magnetic torque on a current loop: The torque exerted on a current-carrying loop of area (A) placed in a uniform magnetic field (B) is given by:
where (\overrightarrow{\mu}) is the magnetic dipole moment of the loop, given by:
These formulas provide additional tools for calculating magnetic fields and forces in various scenarios involving current-carrying wires and coils.
