Moving Charges and Magnetism - Notes

4.1 INTRODUCTION

  • Electricity and magnetism have been known for over 2000 years; their intimate relation was realised around 1820 (Oersted’s discovery).

  • Oersted observed that a current in a straight wire deflects a nearby magnetic compass needle; the needle aligns tangentially to a circle with the wire at its centre and perpendicular to the wire's plane (Fig. 4.1a).

  • Reversing current direction reverses the needle; larger current or closer needle increases deflection; iron filings around the wire form concentric circles about the wire.

  • Conclusion: moving charges (currents) generate a magnetic field around them.

  • In 1864, Maxwell unified electricity and magnetism; he connected these ideas to light as electromagnetic waves; later work by Hertz, Bose, Marconi advanced radio waves.

  • This chapter outlines how magnetic fields exert forces on moving charges and currents, how currents generate magnetic fields, particle acceleration (cyclotron), and detection/measurement devices like galvanometers.

  • Notational conventions introduced:

    • A current or field emerging out of the plane is shown as a dot (
      abla) (a tip of an arrow toward you).

    • A current or field going into the plane is shown as a cross (×) (the tail of an arrow away from you).

  • Fig. 4.1 illustrates the two situations: current out of the plane (dot) and current into the plane (cross).

  • Overview of the upcoming topics: magnetic field concept, Lorentz force, magnetic force on a current-carrying conductor, motion in magnetic field (circular/spiral), Biot–Savart law, axis field of a circular loop, Ampère’s law, solenoids, parallel currents, magnetic dipole torque, moving-coil galvanometers, and related experiments/exercises.

4.2 MAGNETIC FORCE

4.2.1 Sources and fields

  • Recap from Chapter 1: electric field E due to a charge Q is a vector field; the source charge Q produces E at a point r with unit vector
    \hat{r}; the static electric field is given by
    E=14πε0Qr2r^.\mathbf{E} = \frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2}\hat{\mathbf{r}}.

  • A test charge q experiences a force
    F=qE=q14πε0Qr2r^.\mathbf{F} = q\mathbf{E} = q\frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2}\hat{\mathbf{r}}.

  • The field can convey energy and momentum; it propagates with finite speed, not instantaneously; the concept of a field was stressed by Faraday and incorporated by Maxwell.

  • Fields depend on position and can vary with time; in this chapter, the discussion assumes fields may be time-independent for simplicity (