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

Define electrostatic potential at a point.

The work done per unit positive charge in moving it from infinity to that point without acceleration.

How are field and potential related?

\(E=-\dfrac{dV}{dr}\); the field points in the direction of steepest decrease of potential.

What is the potential due to a dipole on its equatorial line?

Zero, because contributions of the two charges cancel at every equatorial point.

Why is no work done in moving a charge on an equipotential surface?

Because the potential difference between any two points on it is zero, so \(W=q\,\Delta V=0\).

What is the field inside a charged conductor in equilibrium?

Zero; all excess charge resides on the outer surface.

Give the capacitance of a parallel-plate capacitor.

\(C=\dfrac{\varepsilon_0 A}{d}\) in vacuum, becoming \(\dfrac{K\varepsilon_0 A}{d}\) with a dielectric.

How does a dielectric change capacitance?

It increases capacitance \(K\) times by reducing the net field between the plates.

How do capacitors add in series?

\(\dfrac{1}{C_s}=\dfrac{1}{C_1}+\dfrac{1}{C_2}+\cdots\); the equivalent is smaller than each.

How do capacitors add in parallel?

\(C_p=C_1+C_2+\cdots\); the equivalent is larger than each.

What is the energy stored in a capacitor?

\(U=\tfrac{1}{2}CV^2=\tfrac{1}{2}QV=\dfrac{Q^2}{2C}\), stored in the field between plates.

Electrostatic Potential and Capacitance

Class 12 Physics · Physics Part I · Chapter 2

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Summary

Electrostatic potential at a point is the work done per unit positive charge in bringing it from infinity to that point, \(V=\dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r}\) for a point charge. Potential is a scalar, making it easier to handle than the field, and the two are linked by \(\vec{E}=-\nabla V\); the field always points from high to low potential. Equipotential surfaces, on which \(V\) is constant, are everywhere perpendicular to field lines, and no work is done moving a charge along them. The electrostatic potential energy of a charge configuration is the total work done in assembling it. A conductor in equilibrium has zero field inside and a constant potential throughout, with charge residing on its surface. Dielectrics, when polarised, reduce the field inside by a factor of the dielectric constant. A capacitor stores charge and energy; its capacitance \(C=Q/V\) depends only on geometry and the dielectric. For a parallel-plate capacitor \(C=\dfrac{\varepsilon_0 A}{d}\), increased \(K\) times by a dielectric. Capacitors in series and parallel combine by reciprocal and direct sums respectively, and the energy stored is \(U=\tfrac{1}{2}CV^2\), residing in the field between the plates.

Electric potential of charges and dipolesEquipotential surfacesPotential energy of charge systemsConductors and dielectricsCapacitance and parallel-plate capacitorCombinations and energy of capacitors

Key terms

Electrostatic potential

Work per unit positive charge to bring it from infinity to a point; scalar, unit volt.

Equipotential surface

A surface of constant potential; the field is perpendicular to it and no work is done along it.

Potential energy

Work done in assembling a charge configuration against electrostatic forces.

Capacitance

Ratio of stored charge to potential, \(C=Q/V\); SI unit farad.

Dielectric constant

Factor \(K\) by which a dielectric reduces the field and raises the capacitance.

Polarisation

Induced dipole moment per unit volume in a dielectric placed in a field.

Extra questions & answers

Try one from this chapter

The electric potential at a point due to a point charge +Q placed in vacuum is V. If the distance of the point from the charge is doubled, the new potential becomes

Flashcards & interactive practice