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.]

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