Review 12-05

Short answer problem 1.

• Use Gauss’s law
• Do spherical integral to find integral of electric field over Gaussian surface
• Set equal to enclosed charge over ${ϵ}_0$.

$$q_{enc}(r)=4\pi {\int }_0^{r}p(r^{{}^{\prime }})r^{{}^{\prime }2}d{r}^{{}^{\prime }}$$

• Non-uniform charge density Short answer problem 2
• DC circuit
• Find current through 6$\Omega$ resistor
• Use Kirchhoff’s loop rule and junction rule
• Choose a direction around both loops and increment EMF through each element of both loops
• Sign convention
• Considering three currents, one on the left, one on right side, and current in the middle resistor Short answer problem 3
• LRC Circuit
• Given values:
  • 45 mH inductor
  • 50 $\Omega$ resistor
  • 30 $\mu F$ capacitor
  • 220 VAC
  • 200 Hz

$$omega=2pi200l=455E-3c=30E-6r=50z=sqrt(r^2+(omega\ast l-(1/(omega\ast c){)}^2))$$

Calculated Inductance ^

There will be drawing rays on final Review Geometric Optics

Concave-Converging-Real Image-Inverted image

Optics bonus question

Three useful rays, one is parallel to optic axis, one going through focal point, one that goes to vertex