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

What are the two basic properties of electric charge besides additivity?

Charge is conserved (total charge of an isolated system is constant) and quantised (\(q=ne\)).

State Coulomb's law in vector form.

\(\vec{F}_{12}=\dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1q_2}{r^2}\hat{r}_{12}\), directed along the line joining the charges.

Why can two electric field lines never intersect?

At an intersection the field would have two directions at one point, which is impossible since \(\vec{E}\) is unique there.

What is the torque on a dipole in a uniform field?

\(\vec{\tau}=\vec{p}\times\vec{E}\), with magnitude \(pE\sin\theta\); the net force is zero.

What is the field of a dipole on its axial line far away?

\(E=\dfrac{1}{4\pi\varepsilon_0}\dfrac{2p}{r^3}\), directed along \(\vec{p}\).

The net electric flux through any closed surface equals \(q_{enc}/\varepsilon_0\), independent of surface shape.

What is the field due to an infinitely long uniformly charged line?

\(E=\dfrac{\lambda}{2\pi\varepsilon_0 r}\), directed radially with linear charge density \(\lambda\).

What is the field due to an infinite charged sheet?

\(E=\dfrac{\sigma}{2\varepsilon_0}\), uniform and independent of distance from the sheet.

What is the field inside a uniformly charged spherical shell?

Zero everywhere inside; outside it behaves as if all charge were at the centre.

Define electric flux and give its SI unit.

It is \(\Phi=\oint\vec{E}\cdot d\vec{A}\); SI unit is N m\(^2\)/C.

Electric Charges and Fields

Class 12 Physics · Physics Part I · Chapter 1

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CBSE Class 12 · Physics

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Summary

Matter carries an intrinsic property called electric charge, which exists in two kinds, positive and negative, and is conserved and quantised as \(q=ne\). Like charges repel and unlike charges attract through a force whose magnitude between two point charges in vacuum obeys Coulomb's law \(F=\dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1q_2}{r^2}\). To describe the influence a charge exerts on its surroundings we introduce the electric field \(\vec{E}=\vec{F}/q_0\), a vector quantity whose direction follows the force on a positive test charge. Field lines give a pictorial map of \(\vec{E}\): they start on positive and end on negative charges, never cross, and crowd together where the field is strong. An electric dipole, two equal and opposite charges separated by a small distance, has a dipole moment \(\vec{p}=q\,2\vec{a}\) and experiences a torque \(\vec{\tau}=\vec{p}\times\vec{E}\) in a uniform field. Electric flux \(\Phi=\oint\vec{E}\cdot d\vec{A}\) measures the field threading a surface, and Gauss's law states the net flux through any closed surface equals the enclosed charge divided by \(\varepsilon_0\). Gauss's law gives elegant results for symmetric distributions: the field of an infinite line, an infinite charged sheet, and a uniformly charged spherical shell.

Charge, conservation and quantisationCoulomb's law and superpositionElectric field and field linesElectric dipole and torqueElectric flux and Gauss's lawApplications of Gauss's law

Key terms

Quantisation of charge

Charge appears only in integral multiples of the elementary charge \(e\), so \(q=ne\).

Coulomb's law

The electrostatic force between two point charges varies as the product of charges and inversely as the square of separation.

Electric field

Force per unit positive test charge at a point, \(\vec{E}=\vec{F}/q_0\), measured in N/C.

Electric dipole moment

Vector \(\vec{p}=q\,2\vec{a}\) directed from the negative to the positive charge.

Electric flux

Scalar product of field and area summed over a surface, \(\Phi=\oint\vec{E}\cdot d\vec{A}\).

Gauss's law

Net flux through a closed surface equals the enclosed charge divided by \(\varepsilon_0\).

Extra questions & answers

Try one from this chapter

Electric charge is quantised. This means the total charge on a body is always:

Flashcards & interactive practice