Class 12 Physics: Moving Charges and Magnetism

Magnetic Field

• Magnetic fields are regions around magnets or electrical currents where magnetic forces can be detected.
• Moving charges or changing electric fields create magnetic fields.
• Magnetic field lines emerge from the north pole and enter the south pole of a magnet.

Biot-Savart Law

• The Biot-Savart law relates the magnetic field dB to the current I, length of wire element dl, and distance r from the wire element.
• dB = (μ₀ * I * dl × r) / (4π * r³)
• μ₀ is the permeability of free space (4π × 10^-7 T·m/A).

Force on a Moving Charge

• A moving charge q experiences a force F in a magnetic field B.
• F = qv × B
• v is the velocity of the charge.
• The direction of the force is perpendicular to both the velocity and the magnetic field.

Force on a Current-Carrying Wire

• A current-carrying wire of length L in a magnetic field B experiences a force F.
• F = IL × B
• I is the current in the wire.
• L is the length of the wire.
• The direction of the force is perpendicular to both the wire and the magnetic field.

Torque on a Current Loop

• A current loop of area A in a magnetic field B experiences a torque τ.
• τ = μ × B
• μ is the magnetic moment (IA).
• The direction of the torque is perpendicular to the plane of the loop.

Electromagnetic Induction

• A changing magnetic flux through a loop of wire induces an electromotive force (EMF).
• ε = -N(dΦ/dt)
• ε is the induced EMF.
• N is the number of turns in the coil.
• Φ is the magnetic flux through the coil.
• The direction of the induced current opposes the change in magnetic flux.