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Charges in an antenna undergo oscillations with amplitude x0 and angular frequency omega. The average power P radiated depends on charge q, x0, omega, epsilon0, and the speed of light c. Using dimensional analysis, the correct expression for P (where a is a dimensionless constant) is:

1. a*q²*omega⁴*x0² / (epsilon0*c²)
2. a*q²*omega⁴*x0² / (epsilon0*c³)
3. a*q⁴*omega²*x0 / (epsilon0²*c⁶)
4. a*q⁴*omega⁴*x0² / (epsilon0²*c⁴)

Correct answer: a*q²*omega⁴*x0² / (epsilon0*c³)

Solution

Setting the dimensions of option B equal to ML²T⁻³ confirms it is the only dimensionally consistent formula for radiated power.

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