A charged particle oscillates about its mean position and radiates electromagnetic waves. The frequency \(\nu_0\) of its oscillation is changed step by step, and the frequency \(\nu\) of the waves is measured each time. The graph of \(\nu\) against \(\nu_0\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → a straight line through the origin with slope 1
An oscillating charge sets up an oscillating electric field. This produces an oscillating magnetic field, and the two fields keep producing each other as the wave moves out. They oscillate at the rate set by the charge, so \( \nu=\nu_0 \).
Option (1) a straight line parallel to the \(\nu_0\)-axis — Incorrect. Such a line would mean the same wave frequency for every \( \nu_0 \). In fact \( \nu \) changes each time \( \nu_0 \) is changed.
Option (2) a rectangular hyperbola — Incorrect. A rectangular hyperbola means that \( \nu \) falls as \( \nu_0 \) rises. That shape belongs to wavelength plotted against frequency, since \( \nu\lambda=c \).
Option (3) a straight line through the origin with slope \(2\pi\) — Incorrect. A slope of \( 2\pi \) comes from mixing up the frequency with the angular frequency \( \omega=2\pi\nu \). Both \( \nu \) and \( \nu_0 \) here are ordinary frequencies.
Option (4) a straight line through the origin with slope 1 — Correct. Since \( \nu=\nu_0 \), the graph is a straight line through the origin with slope 1.
NCERT (2026-27):
Sources of electromagnetic waves – “… Consider a charge oscillating with some frequency. … The oscillating electric and magnetic fields thus regenerate each other, so to speak, as the wave propagates through the space. The frequency of the electromagnetic wave naturally equals the frequency of oscillation of the charge. …”