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