Discussion
Let q and a denote the charge and the acceleration of a moving point charge. Larmor formula states that total power radiated by the point charge is proportional to \(q^{\alpha}a^{\beta}\), where ..............
Answer: D
The radiated power goes as \(q^{2}a^{2}\), so \(\alpha = 2\) and \(\beta = 2\).
The Larmor formula for a non-relativistic accelerated point charge is
\[ \begin{aligned} P &= \frac{\mu_{0}q^{2}a^{2}}{6\pi c} \\ &= \frac{q^{2}a^{2}}{6\pi\varepsilon_{0}c^{3}} \end{aligned} \]
The radiation fields are proportional to \(qa\), and the radiated power, coming from the Poynting vector, goes as the square of the fields. That is why both the charge and the acceleration appear squared, and why the sign of the charge does not matter.
Any option with a first power of \(q\) or \(a\) would make the power change sign with the charge or the direction of acceleration, which a radiated power cannot do.
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