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 did Maxwell introduce displacement current?

To make Ampere's law consistent for charging capacitors, recognising a changing electric field as a source of \(\vec{B}\).

Write the expression for displacement current.

\(I_d=\varepsilon_0\dfrac{d\Phi_E}{dt}\), the rate of change of electric flux times \(\varepsilon_0\).

What is the speed of EM waves in vacuum?

\(c=\dfrac{1}{\sqrt{\mu_0\varepsilon_0}}\approx 3\times10^8\) m/s, the speed of light.

What is the relation between E0 and B0?

\(c=E_0/B_0\); the field amplitudes are in phase and in this fixed ratio.

Do EM waves carry momentum?

Yes; they transport energy and momentum and exert radiation pressure on surfaces.

List the EM spectrum in increasing frequency.

Radio, microwave, infrared, visible, ultraviolet, X-ray, gamma ray.

Give one use of microwaves.

Radar and microwave ovens; they are also used in communication.

Why are X-rays used in medical imaging?

Their short wavelength penetrates soft tissue but is absorbed by bones, giving contrast.

Which radiation is used for sterilisation and why?

Ultraviolet, because its high photon energy destroys micro-organisms.

Electromagnetic Waves

Q: How are E and B oriented in an EM wave?

They are mutually perpendicular and both perpendicular to the direction of propagation; the wave is transverse.

Class 12 Physics · Physics Part I · Chapter 8

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CBSE Class 12 · Physics

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Summary

Maxwell completed the laws of electromagnetism by introducing the displacement current, \(I_d=\varepsilon_0\dfrac{d\Phi_E}{dt}\), recognising that a changing electric field acts as a source of magnetic field, just as a changing magnetic field produces an electric field. This symmetry predicts self-sustaining electromagnetic waves in which oscillating electric and magnetic fields, mutually perpendicular and both perpendicular to the direction of propagation, travel through vacuum at the speed of light \(c=\dfrac{1}{\sqrt{\mu_0\varepsilon_0}}\). The fields are in phase and related by \(c=E_0/B_0\); such waves are transverse and carry energy and momentum, exerting radiation pressure. Light itself is an electromagnetic wave, and the full electromagnetic spectrum—radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays—spans an enormous range of wavelengths and frequencies, all travelling at the same speed in vacuum but produced and detected by different means. Each region has characteristic sources, properties and uses, from radio communication and radar to medical imaging and sterilisation, unifying optics, electricity and magnetism into one grand framework.

Displacement currentMaxwell's synthesisNature of EM wavesEnergy and momentum of EM wavesElectromagnetic spectrumSources and uses of EM radiation

Key terms

Displacement current

Current-like term \(I_d=\varepsilon_0\,d\Phi_E/dt\) from a changing electric field.

Electromagnetic wave

Transverse wave of perpendicular oscillating \(\vec{E}\) and \(\vec{B}\) fields.

Speed of light

Wave speed in vacuum, \(c=1/\sqrt{\mu_0\varepsilon_0}\approx 3\times10^8\) m/s.

Radiation pressure

Pressure exerted by electromagnetic waves carrying momentum.

Electromagnetic spectrum

Ordered range of EM waves from radio to gamma rays.

Transverse wave

Wave whose oscillations are perpendicular to its direction of travel.

Extra questions & answers

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Maxwell introduced the displacement current to account for:

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