Physics 132-04 Test 2


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Questions (5 for 8 pts. apiece) Answer in complete, well-written sentences WITHIN the spaces provided.

  1. Draw what you think the field lines and equipotential lines between parallel plates will look like. Explain you reasoning.








  2. In our simulations of the electric potentials for a point charge and for an electric dipole we found they behaved differently as a function of the distance $r$ from origin. Did the electric dipole potential fall faster, slower, or the same as the point charge? Explain the result you observed.









  3. For a circuit you analyzed like the one shown below how is the voltage drop across $R_1$ related to the potential drop across $R_2$? Explain your observation.





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  4. Consider a situation where there is a uniform magnetic field in space that points in the $y$ direction $\vec B = B\hat j$ and the velocity of a particle with charge $q$ in the field is in the $z$ direction $\vec v = v\hat k$. What is $\theta$ the angle between the magnetic field vector and the velocity vector? What is $\vec F_B$ is terms of the magnitudes of $q$, $v$, and $B$ and the appropriate unit vectors?

  5. Why is it possible for a bird to sit on a high-voltage wire without getting electrocuted?

Problems (3). Clearly show all reasoning for full credit. Use a separate sheet to show your work.

1. 18 pts. Four identical charges are located on the corners of a rectangle as shown in the figure. What is the total, vector electric force exerted on the charge at the lower, right corner in terms of $q$, $L$, $W$, the appropriate unit vectors, and any other necessary constants?



Image 4charges




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2. 18 pts. A rod of length $L$ (see figure) lies along the $x$ axis with its left end at the origin. It has a nonuniform charge density $\lambda = \alpha x$, where $\alpha$ is a positive constant. What is the electric potential at $A$ in terms of $L$, $d$, $\alpha$, and any other necessary constants?



Image lineCharge2

3. 24 pts. A proton ($\rm ^1H$, $m_p=1~u$, $q=e$), a deuteron ($\rm ^2H$, $m_d = 2~u$, $q=e$), and a $\rm ^4He$ nucleus ($m_{He} = 4~u$, $q=2e$) with the same kinetic energies enter a region of uniform magnetic field $\vec B$ moving perpendicular to $\vec B$. What is the ratio of their radii in the magnetic field?





Physics 132-4 Constants


$k_B$ $1.38\times 10^{-23}~J/K$ proton/neutron mass $1.67\times 10^{-27}~kg$
$1 ~ u$ $1.67\times 10^{-27}~kg$ $g$ $9.8~m/s^2$
Gravitation constant $6.67 \times 10^{-11}~N-m^2/kg^2$ Earth's radius $6.37\times 10^6~m$
Coulomb constant ($k_e$) $8.99\times 10^{9} {N-m^2 \over C^2}$ Electron mass $9.11\times 10^{-31}~kg$
Elementary charge ($e$) $1.60\times 10^{-19}~C$ Proton/Neutron mass $1.67\times 10^{-27}~kg$
Permittivity constant ($\epsilon_0$) $8.85\times 10^{-12} {kg^2\over N-m^2}$ $\rm 1.0~eV$ $1.6\times 10^{-19}~J$
$\rm 1 ~MeV$ $10^6 ~ eV$ atomic mass unit ($u$) $1.66\times 10^{-27}~kg$


Physics 132-4 Equations



\begin{displaymath} \vec F_C = k_e \frac{q_1 q_2}{r^2} \hat r \qquad \vec E \equ... ...over r_i^2} \hat r_i \qquad \vec E = \int \frac{dq}{r^2}\hat r \end{displaymath}


\begin{displaymath} \vec E_{plate} = 2 \pi k_e \sigma \hat k = \frac{\sigma}{2\e... ...d \vec E_{ring} = k_e \frac{qx}{(x^2 + R^2)^{3/2}} \hat {i\,} \end{displaymath}


\begin{displaymath} W \equiv \int \vec F \cdot d\vec s \quad \Delta V \equiv {\D... ... V = k_e {q\over r} \quad V = k_e \sum_n {q_n \over r_n} \quad \end{displaymath}


\begin{displaymath} V = k_e \int {dq \over r} \quad V = Ed \quad E_x = - {\parti... ...artial z} \quad V = \frac{k_e p \cos\theta}{r^2} \quad p = 2aq \end{displaymath}


\begin{displaymath} I \equiv {dQ \over dt} \qquad V = IR \qquad P = IV \qquad R_{equiv} = \sum R_i \qquad {1 \over R_{equiv}} = \sum {1\over R_i} \end{displaymath}


=100000

=2.5in The algebraic sum of the potential changes across all the elements of a closed loop is zero. The sum of the currents entering a junction is equal to the sum of the currents leaving the junction.



\begin{displaymath} I = n e v_d A \quad v_d = \frac{eE\tau}{m_e} \quad R = \fra... ...d \langle E \rangle = \frac{1}{2}mv_{rms}^2 = \frac{3}{2}k_B T \end{displaymath}


\begin{displaymath} \vec F_B = q \vec v \times \vec B \qquad \vert\vec F_B\vert... ...vB\sin \theta \vert \qquad \vert\vec F_c\vert = m\frac{v^2}{r} \end{displaymath}


\begin{displaymath} KE_0 + PE_0 = KE_1 + PE_1 \quad KE = {1 \over 2} m v^2 \quad PE = qV \end{displaymath}


\begin{displaymath} \vec F=m \vec a \qquad x = \frac{a}{2} t^2 + v_0 t + x_0 \qquad v = at + v_0 \end{displaymath}


\begin{displaymath} {dx^n \over dx} = nx^{n-1} \qquad {d f(u) \over dx} = {df\ov... ... \ \over dx} f(x)\cdot g(x) = f{dg \over dx} + g{df \over dx} \end{displaymath}


\begin{displaymath} \langle x\rangle = \frac{1}{N}\sum_i x_{i} \quad \sigma = \s... ...} \quad A = 4\pi r^2 \quad V = Ah \quad V = {4\over 3} \pi r^3 \end{displaymath}


\begin{displaymath} \frac{d f(x)}{dx} = \lim_{\Delta x \rightarrow 0} \frac{f(x+... ...elta x} \quad \frac{df(y)}{dx} = \frac{df(y)}{dy}\frac{dy}{dx} \end{displaymath}


\begin{displaymath} \int \frac{1}{x} dx = \ln x \quad \int x^{n} dx = \frac{x^{n+1}}{n+1} \quad \int e^x dx = e^x \end{displaymath}

Image periodicChart



The Periodic Chart.