CBSE Class 12 — Notes, Chapters & Practice Quizzes

Chapter 4: Moving Charges and Magnetism

Summary

A moving charge experiences a magnetic force \(\vec{F}=q\vec{v}\times\vec{B}\), perpendicular to both velocity and field, doing no work and causing circular or helical motion. Combined with the electric force it gives the Lorentz force \(\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})\). The Biot-Savart law gives the field of a current element, \(d\vec{B}=\dfrac{\mu_0}{4\pi}\dfrac{I\,d\vec{l}\times\hat{r}}{r^2}\), from which the field of a circular loop and a straight wire follow. Ampere's circuital law, \(\oint\vec{B}\cdot d\vec{l}=\mu_0 I_{enc}\), elegantly yields the field of a long solenoid \(B=\mu_0 nI\) and a toroid. A current-carrying conductor in a field feels \(\vec{F}=I\vec{l}\times\vec{B}\), and two parallel currents attract or repel, defining the ampere. A current loop behaves as a magnetic dipole with moment \(\vec{m}=I\vec{A}\), experiencing torque \(\vec{\tau}=\vec{m}\times\vec{B}\)—the principle of the moving-coil galvanometer. With suitable shunt or series resistance, a galvanometer is converted into an ammeter or voltmeter.

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