Quiz 4 (Friday Feb. 28)

• Maxwell Ampere + Poynting Vector
  • Determine the electric and magnetic field in a situation where there is a displacement current
  • Discuss the direction of the Poynting vector and how it relates to conservation of energy

Papers

• Due next Friday (Feb. 28) by 5pm (20% of your grade BTW)

A function, $f(x,t)$, satisfies this PDE:

$$\dfrac{\partial^2 f}{\partial x^2} = \dfrac{1}{c^2}\dfrac{\partial^2 f}{\partial t^2}$$

Which of the following functions work?

1. $\sin( k(x – vt))$
2. $exp( k(-x – vt ))$
3. $a( x + vt )^3$
4. All of these.
5. None of these.

A "right moving" solution to the wave equation is:

$$f_R(z,t) = A \cos(kz – \omega t + \delta)$$

Which of these do you prefer for a "left moving" soln?

1. $f_L(z,t) = A \cos(kz + \omega t + \delta)$
2. $f_L(z,t) = A \cos(kz + \omega t - \delta)$
3. $f_L(z,t) = A \cos(-kz – \omega t + \delta)$
4. $f_L(z,t) = A \cos(-kz – \omega t - \delta)$
5. more than one of these!

(Assume $k, \omega, \delta$ are positive quantities)

Two different functions $f_1(x,t)$ and $f_2(x,t)$ are solutions of the wave equation.

$$\dfrac{\partial^2 f}{\partial x^2} = \dfrac{1}{c^2}\dfrac{\partial^2 f}{\partial t^2}$$

Is $(A f_1 + B f_2 )$ also a solution of the wave equation?

1. Yes, always
2. No, never
3. Yes, sometimes depending on $f_1$ and $f_2$

Two traveling waves 1 and 2 are described by the equations:

$$y_1(x,t) = 2 \sin(2x – t)$$ $$y_2(x,t) = 4 \sin(x – 0.8 t)$$

All the numbers are in the appropriate SI (mks) units.

Which wave has the higher speed?

1. 1
2. 2
3. Both have the same speed

Two impulse waves are approaching each other, as shown. Which picture correctly shows the total wave when the two waves are passing through each other?

A solution to the wave equation is: $$f(z,t) = A \cos(kz – \omega t + \delta)$$

• What is the speed of this wave?
• Which way is it moving?
• If $\delta$ is small (and >0), is this wave "delayed" or "advanced"?
• What is the frequency?
• The angular frequency?
• The wavelength?
• The wave number?

A solution to the wave equation is: $$f(z,t) = Re\left[A e^{i(kz – \omega t + \delta)}\right]$$

• What is the speed of this wave?
• Which way is it moving?
• If $\delta$ is small (and >0), is this wave "delayed" or "advanced"?
• What is the frequency?
• The angular frequency?
• The wavelength?
• The wave number?

A complex solution to the wave equation in 3D is:

$$\widetilde{f}(\mathbf{r},t) = \widetilde{A}e^{i(\mathbf{k}\cdot\mathbf{r}-\omega t)}$$

• What is the speed of this wave?
• Which way is it moving?
• Why is there no $\delta$?
• What is the frequency?
• The angular frequency?
• The wavelength?
• The wave number?