<img src="./images/capacitor_gauss_D.png" align="right" style="width: 300px";/> An ideal (large) capacitor has charge $Q$. A neutral linear dielectric is inserted into the gap. We want to find $\mathbf{D}$ in the dielectric. $$\oint \mathbf{D}\cdot d\mathbf{A} = Q_{free}$$ What is $|\mathbf{D}|$ in the dielectric? 1. $\sigma$ 2. $2\sigma$ 3. $\sigma/2$ 4. $\sigma+\sigma_b$ 5. Something else Note: * CORRECT ANSWER: A

<img src="./images/capacitor_Q_dielectric.png" align="right" style="width: 300px";/> An ideal (large) capacitor has charge $Q$. A neutral linear dielectric is inserted into the gap. Now that we have $\mathbf{D}$ in the dielectric, what is $\mathbf{E}$ inside the dielectric? 1. $\mathbf{E} = \mathbf{D} \varepsilon_0 \varepsilon_r$ 2. $\mathbf{E} = \mathbf{D}/\varepsilon_0 \varepsilon_r$ 3. $\mathbf{E} = \mathbf{D} \varepsilon_0$ 4. $\mathbf{E} = \mathbf{D}/\varepsilon_0$ 5. Not so simple! Need another method Note: * CORRECT ANSWER: B

A point charge $+q$ is placed at the center of a neutral, linear, homogeneous, dielectric teflon shell. Can $\mathbf{D}$ be computed from its divergence? <img src="./images/teflon_shell_D.png" align="left" style="width: 300px";/> $$\oint \mathbf{D} \cdot d\mathbf{A} = Q_{free}$$ 1. Yes 2. No 3. Depends on other things not given

A point charge $+q$ is placed at the center of a neutral, linear, homogeneous, dielectric **hemispherical** shell. Can $\mathbf{D}$ be computed from its divergence? <img src="./images/teflon_hemisphere_dielectric.png" align="left" style="width: 300px";/> $$\oint \mathbf{D} \cdot d\mathbf{A} = Q_{free}$$ 1. Yes 2. No 3. Depends on other things not given

## Boundary Conditions <img src="./images/air-material-boundary-tutorial.png" align="center" style="width: 500px";/>

## Why are these boundary conditions useful? <img src="./images/cap_w_2_dielectrics.png" align="center" style="width: 500px";/>