Solution Found!
In Ex. 11.3 we assumed the velocity and acceleration were
Chapter 11, Problem 16P(choose chapter or problem)
Problem 16P
In Ex. 11.3 we assumed the velocity and acceleration were (instantaneously, at least) collinear. Carry out the same analysis for the case where they are perpendicular. Choose your axes so that v lies along the z axis and a along the x axis (Fig. 11.14), so that Check that P is consistent with the Liénard formula
Figure 11.14 and 11.5
For relativistic velocities (β ≈ 1) the radiation is again sharply peaked in the forward direction (Fig. 11.15). The most important application of these formulas is to circular motion—in this case the radiation is called synchrotron radiation. For a relativistic electron, the radiation sweeps around like a locomotive’s headlight as the particle moves.]
Questions & Answers
QUESTION:
Problem 16P
In Ex. 11.3 we assumed the velocity and acceleration were (instantaneously, at least) collinear. Carry out the same analysis for the case where they are perpendicular. Choose your axes so that v lies along the z axis and a along the x axis (Fig. 11.14), so that Check that P is consistent with the Liénard formula
Figure 11.14 and 11.5
For relativistic velocities (β ≈ 1) the radiation is again sharply peaked in the forward direction (Fig. 11.15). The most important application of these formulas is to circular motion—in this case the radiation is called synchrotron radiation. For a relativistic electron, the radiation sweeps around like a locomotive’s headlight as the particle moves.]
ANSWER:
Solution 16P
Step 1 of 2:
In this question, we need to carry out an analysis such that velocity and acceleration are perpendicular
We need to choose axis such that lies along the
axis and
along the
axis
Such that
and
We also need to check if is consistent with Lienard formula
That is