Moving Charges and Magnetism
Class 12 Physics · Physics Part I · Chapter 4
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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.
Magnetic force and Lorentz forceMotion of charges in fieldsBiot-Savart and Ampere's lawsSolenoid and toroidForce on conductors and parallel currentsTorque, magnetic moment and galvanometer
Key terms
Lorentz force
Total electromagnetic force on a charge, \(\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})\).
Biot-Savart law
Gives the field of a current element, \(dB=\dfrac{\mu_0}{4\pi}\dfrac{I\,dl\sin\theta}{r^2}\).
Ampere's circuital law
Line integral of \(\vec{B}\) around a closed loop equals \(\mu_0 I_{enc}\).
Magnetic moment
Property of a current loop, \(\vec{m}=I\vec{A}\); SI unit A m\(^2\).
Solenoid
A coil whose interior field is uniform, \(B=\mu_0 nI\).
Galvanometer
Device detecting small currents via torque on a coil in a radial field.
Extra questions & answers
Try one from this chapter
The magnetic force on a charge moving with velocity v in field B is: