Calculate the electromagnetic radiation emitted by an electron undergoing non-uniform circular motion. Determine the power radiated, the angular distribution of radiation, and the rate of energy loss due to radiation.
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To calculate the electromagnetic radiation emitted by an electron undergoing non-uniform circular motion, we need to consider the acceleration of the electron and its corresponding radiation pattern.
1. Power radiated:
The power radiated by an accelerated charge can be calculated using the Larmor formula:
P = (2/3) * (q^2 * a^2) * (c^3) / (4 * pi * e0)
where:
P is the power radiated
q is the charge of the electron
a is the acceleration of the electron
c is the speed of light in a vacuum
pi is the mathematical constant pi
e0 is the permittivity of free space
2. Angular distribution of radiation:
The radiation pattern produced by an accelerated charge is given by the Lienard-Wiechert potentials. However, the exact expression for the angular distribution depends on the specific motion of the electron. It would require knowledge of the trajectory of the electron or the detailed time-varying acceleration to determine the angular distribution of radiation.
3. Rate of energy loss due to radiation:
The rate of energy loss due to radiation can be calculated by integrating the power radiated over time. If we assume the acceleration and motion of the electron are time-varying, we can integrate the power radiated over the appropriate time period to find the total energy loss.
It's important to note that finding the exact calculations for the power radiated, angular distribution, and energy loss due to radiation in the case of non-uniform circular motion is a complex problem that requires detailed knowledge of the acceleration and motion of the electron.
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