What traumatic event does Zitkala-Sa describe at the school?

The forcible cutting of her long hair

Why was the cutting of her hair so humiliating to Zitkala-Sa?

Among her people, shingled hair was worn by cowards and mourners

Why does the magnetic force do no work on a charge?

Because \(\vec{F}=q\vec{v}\times\vec{B}\) is always perpendicular to velocity, so \(\vec{F}\cdot\vec{v}=0\).

Write the Lorentz force expression.

\(\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})\), the combined electric and magnetic force.

State the Biot-Savart law.

\(d\vec{B}=\dfrac{\mu_0}{4\pi}\dfrac{I\,d\vec{l}\times\hat{r}}{r^2}\) for the field of a small current element.

What is the field at the centre of a circular current loop?

\(B=\dfrac{\mu_0 I}{2R}\), perpendicular to the plane of the loop.

State Ampere's circuital law.

\(\oint\vec{B}\cdot d\vec{l}=\mu_0 I_{enc}\), where \(I_{enc}\) is the net current enclosed.

What is the field inside a long solenoid?

\(B=\mu_0 nI\), uniform along the axis, where \(n\) is turns per unit length.

What is the force between two parallel current-carrying wires?

\(\dfrac{F}{l}=\dfrac{\mu_0 I_1 I_2}{2\pi d}\); like currents attract, unlike repel.

What is the torque on a current loop in a magnetic field?

\(\vec{\tau}=\vec{m}\times\vec{B}\), magnitude \(mB\sin\theta\) with \(m=NIA\).

How is a galvanometer converted into an ammeter?

By connecting a low resistance (shunt) in parallel with the coil.

How is a galvanometer converted into a voltmeter?

By connecting a high resistance in series with the coil.

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:

Flashcards & interactive practice