Simple Nature - Light and Matter

backward-time universe, all the momenta are reversed, but that just negates both sides of the

equation, so momentum is still conserved.

Page 758, problem 54:

Note that in the Biot-Savart law, the variableris defined as a vector that points from the

current to the point at which the field is being calculated, whereas in the polar coordinates used

to express the equation of the spiral, the vector more naturally points the opposite way. This

requires some fiddling with signs, which I’ll suppress, and simply identify d`with dr.

B=

kI

c^2

∫

d`×r

r^3

The vector drhas components dx=w(cosθ−θsinθ) and dy=w(sinθ+θcosθ). Evaluating
the vector cross product, and substitutingθ/wforr, we find

B=

kI

c^2 w

∫

θ(cosθsinθ−θsin^2 θ−cosθsinθ−θcos^2 θ) dθ

θ^3

=

kI

c^2 w

∫

dθ

θ

=

kI

c^2 w

ln

θ 2

θ 1

=

kI

c^2 w

ln

b

a

Solutions for chapter 12

Page 827, problem 4:

Because the surfaces are flat, you get specular reflection. In specular reflection, all the reflected

rays go in one direction. Unless the plane is directly overhead, that direction won’t be the right

direction to make the rays come back to the radar station.

This is different from a normal plane, which has complicated, bumpy surfaces. These surfaces

give diffuse reflection, which spreads the reflected rays randomly in more or less every possible

direction.

Page 827, problem 5:

It spells “bonk.”