<img src="./images/5_locations_charging_cap.png" align="left" style="width: 400px";/> Let's return to the complete definition of Ampere's Law: $\nabla \times \mathbf{B} = \mu_0\mathbf{J} + \varepsilon_0 \mu_0 \frac{d\mathbf{E}}{dt}$. **At location 1**, what are the signs of $J_x$, $dE_x/dt$, and $(\nabla \times \mathbf{B})_x$? 1. $J_x<0$, $dE_x/dt<0$, $(\nabla \times \mathbf{B})_x<0$ 2. $J_x=0$, $dE_x/dt>0$, $(\nabla \times \mathbf{B})_x>0$ 3. $J_x>0$, $dE_x/dt=0$, $(\nabla \times \mathbf{B})_x>0$ 4. $J_x>0$, $dE_x/dt>0$, $(\nabla \times \mathbf{B})_x>0$ 5. Something else Note: * Correct Answer: C * There's no E there, Jx points to the right

<img src="./images/5_locations_charging_cap.png" align="left" style="width: 400px";/> Let's return to the complete definition of Ampere's Law: $\nabla \times \mathbf{B} = \mu_0\mathbf{J} + \varepsilon_0 \mu_0 \frac{d\mathbf{E}}{dt}$. **At location 3**, what are the signs of $J_x$, $dE_x/dt$, and $(\nabla \times \mathbf{B})_x$? 1. $J_x<0$, $dE_x/dt<0$, $(\nabla \times \mathbf{B})_x<0$ 2. $J_x=0$, $dE_x/dt>0$, $(\nabla \times \mathbf{B})_x>0$ 3. $J_x>0$, $dE_x/dt=0$, $(\nabla \times \mathbf{B})_x>0$ 4. $J_x>0$, $dE_x/dt>0$, $(\nabla \times \mathbf{B})_x>0$ 5. Something else Note: * Correct Answer: B * There's no Jx there, Ex points to the right

<img src="./images/capacitor_with_x.png" align="left" style="width: 400px";/> A pair of capacitor plates are charging up due to a current $I$. The plates have an area $A=\pi R^2$. Use the Maxwell-Ampere Law to find the magnetic field at the point "x" in the diagram as distance $r$ from the wire. 1. $B = \frac{\mu_0 I}{4 \pi r}$ 2. $B = \frac{\mu_0 I}{2 \pi r}$ 3. $B = \frac{\mu_0 I}{4 \pi r^2}$ 4. $B = \frac{\mu_0 I}{2 \pi r^2}$ 5. Something much more complicated Note: * Correct Answer: B

<img src="./images/capacitor_with_x.png" align="left" style="width: 400px";/> The plates have an area $A=\pi R^2$. Use the Gauss' Law to find the electric field between the plates, answer in terms of $\sigma$ the charge density on the plates. 1. $E = \sigma/\varepsilon_0$ 2. $E = -\sigma/\varepsilon_0$ 3. $E = \sigma/(\varepsilon_0 \pi R^2)$ 4. $E = \sigma \pi R^2 / \varepsilon_0$ 5. Something much more complicated Note: * Correct Answer: B

<img src="./images/capacitor_with_x.png" align="left" style="width: 400px";/> The plates have an area $A=\pi R^2$. Determine the relationship between the current flowing in the wires and the rate of change of the charge density on the plates. 1. $d\sigma/dt = I$ 2. $\pi R^2 d\sigma/dt = I$ 3. $d\sigma/dt = \pi R^2 I$ 4. Something else Note: * Correct Answer: B

We found the relationship between the current and the change of the charge density was: $\pi R^2 d\sigma/dt = I$. Determine the rate of change of the electric field between the plates, $d\mathbf{E}/dt$. 1. $\sigma/\varepsilon_0 \hat{x}$ 2. $I/(\pi R^2 \varepsilon_0) \hat{x}$ 3. $-I/(\pi R^2 \varepsilon_0) \hat{x}$ 4. $I/(2 \pi R \varepsilon_0) \hat{x}$ 5. $-I/(2 \pi R \varepsilon_0) \hat{x}$ Note: * Correct Answer: B

<img src="./images/capacitor_face_on.png" align="left" style="width: 400px";/> Use the Maxwell-Ampere Law to derive a formula for the manetic at a distance $r<R$ from the center of the plate in terms of the current, $I$. 1. $B=\frac{\mu_0 I}{2\pi r}$ 2. $B=\frac{\mu_0 I r}{2\pi R^2}$ 3. $B=\frac{\mu_0 I}{4\pi r}$ 4. $B=\frac{\mu_0 I r}{4\pi R^2}$ 5. Something else entirely Note: * Correct Answer: B

<img src="./images/capacitor_face_on.png" align="left" style="width: 400px";/> Use the Maxwell-Ampere Law to derive a formula for the manetic at a distance $r>R$ from the center of the plate in terms of the current, $I$. 1. $B=\frac{\mu_0 I}{2\pi r}$ 2. $B=\frac{\mu_0 I r}{2\pi R^2}$ 3. 0 5. Something else entirely Note: * Correct Answer: A