The work energy theorem states:
$$W = \int_i^f \mathbf{F}net\cdot d\mathbf{l} = \frac{1}{2}mv_f^2 - \frac{1}{2} mv_i^2$$
This theorem is valid:
1. only for conservative forces.
2. only for non-conservative forces.
3. only for forces which are constant in time
4. only for forces which can be expressed as potential energies
5. for all forces.
Note:
* Correct Answer: E
A + and - charge are held a distance R apart and released.
The two particles accelerate toward each other as a result of the Coulomb attraction. As the particles approach each other, the energy contained in the electric field surrounding the two charges...
<img src="./images/two_charges_coming_together.png" align="center" style="width: 600px";/>
1. increases
2. decreases
3. stays the same
Note:
* Correct Answer: B
The time rate of change of the energy density is,
$\frac{\partial}{\partial t} u
_q = -\frac{\partial}{\partial t}(\frac{\varepsilon_0}{2}E^2 + \frac{1}{2\mu_0}B^2)-\nabla \cdot \mathbf{S}$
where $\mathbf{S} = \frac{1}{\mu_0}\mathbf{E} \times \mathbf{B}$.
How do you interpret this equation? In particular: Does the minus sign on the first term on the right seem ok?
1. Yup
2. It's disconcerting, did we make a mistake?
3. ??
Note:
* Correct Answer: A
* Talk about the signs with them
If we integrate the energy densities over a closed volume, how would interpret $\mathbf{S}$?
$$\frac{\partial}{\partial t}\iiint (u_q + u_E)d\tau = -\iiint \nabla \cdot \mathbf{S} d\tau$$
1. OUTFLOW of energy/area/time or
2. INFLOW of energy/area/time
3. OUTFLOW of energy/volume/time
4. INFLOW of energy/volume/time
5. ???
Note:
* Correct Answer: A
If we integrate the energy densities over a closed volume, how would interpret $\mathbf{S}$?
$$\frac{\partial}{\partial t}\iiint (u_q + u_E)d\tau = -\iiint \nabla \cdot \mathbf{S} d\tau = - \iint \mathbf{S} \cdot d\mathbf{A}$$
1. OUTFLOW of energy/area/time or
2. INFLOW of energy/area/time
3. OUTFLOW of energy/volume/time
4. INFLOW of energy/volume/time
5. ???
Note:
* Correct Answer: A