Formulary - Exam 3

$$n_1\sin\phi_1=n_2\sin\phi_2$$       $$n=\frac{\text{speed of light in a vacuum}}{\text{speed of light in material}}$$   $$\phi_c =\arcsin(n_1/n_2)$$
$$m= \frac{h'}{h}=-\frac{s'}{s}$$ $$\frac{1}{f}=\frac{1}{s}+\frac{1}{s'}$$       $$M=\frac{\theta'}{\theta}=\frac{25 \text{ cm}}{f}=\frac{f_o}{f_e}$$
$$\frac{2}{R}=\frac{1}{f}$$ $$\frac{1}{f}=(n-1)\left[\frac{1}{R_1}+\frac{1}{R_2}\right]$$  
$$m\lambda=d\sin\theta$$ $$\sin\theta=\lambda/a$$ $$\alpha=1.22\lambda/a$$

 

You should know:

The final will concentrate (60-70% of it) on the most recent material from chapters 32-36. The remainder will be drawn from earlier parts of the course.

Of this earlier material (30-40% of the exam) there will *certainly* be a problem using Ampere's Law, and one involving series/parallel resistances.

 

Formulary - Exam 2

$$I=\frac{1}{R} V$$       $$\myv B = \int d\myv B=\int \frac{\mu_0}{4\pi}\frac{I\,d\myv \ell \times \uv r}{r^2}$$
$$R=\rho \frac{l}{A}$$ $$\myv F_m = q \myv v \times \myv B=I\myv \ell\times \myv B$$       $$\myv B = \frac{\mu_0}{4\pi}\frac{q\myv v\times \uv r}{r^2}$$
$$P=VI$$
$$ P_\text{ave}=V_\text{RMS}I_\text{RMS}$$
$$B=\frac{\mu_0 I}{4\pi}\frac{2a}{x\sqrt{x^2+a^2}}=\frac{\mu_0 I}{2\pi x}\sin \theta_\text{max}$$ $$\omega_\text{cyc} = \frac{qB_\perp}{m}$$
$$\myv A \times \myv B \equiv AB\sin\theta \,\uv{n}$$ $$\Phi_m =\int_{\cal S}B_\perp\,da$$ $$\mu_0=4\pi\times10^{-7}T\cdot m/A$$
$$B=\mu_0nI$$ $$\oint \myv B\cdot d\myv \ell =\oint B_\parallel\,d\ell= \mu_0 I_\text{enc}$$ $$B=\frac{\mu_0 I a^2}{2(x^2+a^2)^{3/2}}$$
$$\mu=I*A$$ $$M=\frac{N_2\Phi_2}{i_1}=\frac{N_1\Phi_1}{i_2}$$ $${\cal E}=-N\frac{d\Phi}{dt}=L\frac{di}{dt}$$
$$U=-\myv \mu \cdot \myv B=\mu B \cos\theta$$ $${\cal E}=vBL$$ $${\cal E}=\oint \myv E \cdot d\myv \ell = -\frac{d\Phi_m}{dt}$$
$$V_\text{RMS}=V/\sqrt 2$$ $$\tau=L/R$$ $$\tau=1/RC$$
$$I=nqv_DA$$ $$e=1.6\times 10^{-19}\,\text{C}$$ $$m_e=9.109\times 10^{-31}\,\text{kg}$$

 

You should know:

You will not need to review dielectrics, after all.

Formulary - Exam 1

$$\myv F=k\frac{qQ}{r^2}\uv r$$       $$k=\frac{1}{4\pi \epsilon_0}=9\times 10^9\frac{N\cdot m^2}{C^2}$$
$$\oint E_\perp \,dA=\frac{q}{\epsilon_0}$$ $$\Phi=\int_{\cal S} E_\perp dA$$       $$U=qV$$
$$\myv E=k\frac{q}{r^2}\uv r$$ $$\myv E=\frac{k\lambda}{2}\frac{1}{s}\uv s$$ $$\myv E=2\pi k\sigma\frac{\myv z}{|z|}$$
$$\Delta V = -\int \myv E \cdot d \myv l$$ $$V=k\frac{Q}{r}$$ $$Q=CV$$
$$u=\frac{1}{2}\epsilon_0 |E^2|$$ $$e=1.6\times 10^{-19}\,\text{C}$$ $$m_e=9.109\times 10^{-31}\,\text{kg}$$