Magnetic Fields & Forces – Moving Charges & Currents Explained | Chapter 27 of University Physics

Chapter 27 dives into how moving charges and currents generate and respond to magnetic fields. From the fundamental Lorentz force to real-world applications like mass spectrometers and DC motors, you’ll build the foundation for electromagnetism.

Watch the full video summary on YouTube for demonstrations of magnetic forces and device applications.

Fundamentals of Magnetism

Magnetic fields arise from moving electric charges. Every magnet has a north and south pole—no isolated monopoles exist. In practice, charges create the field, then other moving charges feel a force within it.

The Magnetic Field (B)

The magnetic field B is a vector field measured in tesla (T), with lines forming closed loops from north to south poles. Field line density indicates strength, and a compass aligns with the local field direction.

Magnetic Force on a Moving Charge

The Lorentz force law governs motion:

F = q v × B, with magnitude F = |q| v B sin φ. The force is perpendicular to both velocity v and field B (right-hand rule) and does no work, altering direction but not speed.

Motion of Charged Particles

Circular Motion

If velocity is ⟂ to B, particles move in circles:

• Radius: r = m v / (|q| B)
• Angular speed: ω = |q| B / m

Helical Motion

Combining parallel and perpendicular velocity components produces a helical trajectory—circular motion superimposed on uniform translation along B.

Applications: Velocity Selector & Mass Spectrometer

• Velocity selector: crossed E and B fields filter particles satisfying v = E / B.
• Mass spectrometer: charged particles follow circular paths where r ∝ m / q, enabling precise mass-to-charge ratio analysis.

Force on Current-Carrying Wires

A wire of length l carrying current I in a magnetic field experiences:

F = I l × B. For curved wires, integrate dF = I dl × B. This principle drives speakers and electric motors.

Magnetic Dipole Moment & Torque

A current loop acts as a magnetic dipole with moment M = I A. In a field, it experiences a torque:

τ = M × B, magnitude τ = M B sin φ, and potential energy U = –M · B, minimized when aligned.

DC Motors & Back EMF

DC motors convert electrical energy to mechanical work. Key parts include rotor coils, a stator field, commutator, and brushes. As the rotor spins, a back emf is induced opposing the supply voltage, regulating current and speed.

The Hall Effect

When current flows through a conductor in a magnetic field, charge carriers deflect sideways, creating a Hall voltage. Measuring this transverse voltage reveals carrier type, density, and drift velocity. The relation n q = J_x B_y / E_z links these quantities.

Conclusion

Chapter 27 bridges electricity and magnetism through moving charges and fields. Master the Lorentz force, particle trajectories, and device applications to tackle advanced topics like electromagnetic induction and Maxwell’s equations.

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