Learn Extracted exam questions AP Physics C: Electricity and Magnetism 2016 Free Response
2016 Free Response
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Two point charges, $q_1$ and $q_2$, are fixed in place on the $x$-axis at positions $x_1 = -1.00\text{ m}$ and $x_2 = +0.50\text{ m}$, respectively. Charge $q_2$ has a value of $+2.0\text{ nC}$. Values of electric potential are illustrated by the given equipotentials in the diagram shown above, which is drawn to scale.
[Diagram: A set of equipotential curves in the $xy$-plane (drawn to scale, grid spacing $0.5$ m per square as shown by the "0.5 m" scale bar). The $x$-axis runs horizontally with charge $q_1 = {}?$ marked as a filled dot on the negative $x$-axis and charge $q_2 = 2.0\text{ nC}$ marked as a filled dot at $x = +0.50$ m. Points $A$ and $B$ lie on the $x$-axis just to the right of $q_2$, with $B$ to the right of $A$. Point $E$ lies on the $x$-axis far to the right, at the crossing of the $-4$ V and $0$ V equipotential curves. Point $C$ is above and to the left of the $y$-axis, inside the $-8$ V curve near the top. Point $D$ is to the left of the $y$-axis, between the $-16$ V and $-20$ V curves. The labeled equipotential curves, from outside in (left family) are $-12$ V, $-16$ V, $-20$ V, $-24$ V (nested curves opening around $q_1$ and extending to enclose part of the region left of the $y$-axis), and (right family, nested around $q_2$) $-8$ V, $-4$ V, $+8$ V, $+4$ V, $0$ V. The $0$ V curve is the innermost closed curve immediately surrounding $q_2$, passing near points $A$/$B$.]
Calculate the value of $q_1$.
At point $C$ on the diagram, draw a vector representing the direction of the electric field at that point.
Calculate the approximate magnitude of the electric field strength at point $D$ on the diagram.
The equipotential labeled $0$ V is the cross section of a nearly spherical surface. Calculate the electric flux for this surface.
A proton is placed at point $A$ and then released from rest. Calculate the work done by the electric field on the proton as it moves from point $A$ to point $E$.
Calculate the speed of the proton when it reaches point $E$.
An electron is released from rest at point $B$. Which of the following indicates the direction of the initial acceleration, if any, of the electron?
_____ Up _____ Down _____ Left _____ Right _____ Into the page _____ Out of the page _____ The direction is undefined since the acceleration is zero.
Justify your answer.
[Circuit diagram: A rectangular circuit loop. The top branch contains an ideal voltmeter $V$ in parallel with a resistor of resistance $R$ (drawn as a resistor symbol labeled $R$, with the voltmeter $V$ connected across it above). The left branch contains a source of variable emf $\mathcal{E}$ (battery symbol with an arrow through it, indicating variability). The right branch contains a sample of wire with resistance $r$ (resistor symbol labeled $r$). The bottom branch contains an ideal ammeter $A$. All four branches connect the loop in series around the rectangle.]
The circuit shown above consists of a source of variable emf $\mathcal{E}$, an ideal ammeter A, an ideal voltmeter V, a resistor of resistance $R$, and a sample of wire with resistance $r$.
How does the current through the wire sample compare with the current through the resistor $R$?
_____ It is greater through $R$. _____ It is greater through the sample. _____ It is the same through both. _____ It depends on the resistance of the sample.
Justify your answer.
How does the potential difference across the wire sample compare with the potential difference across the resistor $R$?
_____ It is greater across $R$. _____ It is greater across the sample. _____ It is the same across both. _____ It depends on the resistance of the sample.
Justify your answer.
With the sample of wire in place, the emf of the source is set to a given value. The current through and potential difference across the resistor $R$ are measured. This is repeated for several values of emf, and the data are recorded in the table below.
| $\mathcal{E}$ (V) | $V_R$ (V) | $I_R$ (A) |
|---|---|---|
| 0.250 | 0.179 | 0.162 |
| 0.500 | 0.335 | 0.327 |
| 0.750 | 0.520 | 0.490 |
| 1.000 | 0.670 | 0.687 |
Indicate below which quantities should be graphed to yield a straight line that could be used to calculate a numerical value for the resistance of the wire sample.
Horizontal axis: _____________
Vertical axis: _____________
You may use the remaining columns in the table above, as needed, to record any quantities that you indicated that are not given.
On the grid below, plot the straight line data points from part (c). Clearly scale and label all axes, including units if appropriate. Draw a straight line that best represents the data.
[Blank graphing grid with fine gridlines, approximately square, no axes labeled — for the student to scale, label, and plot on.]
Use your straight line to calculate the value of the resistance of the wire sample.
The wire sample has a length of $3.00\text{ m}$ and a radius of $1.00 \times 10^{-3}\text{ m}$. Calculate the resistivity of the material from which the wire sample is made.
Suppose the ammeter used to collect these data was not ideal. Would the actual value of the resistance of the wire sample be greater than, less than, or equal to that calculated in part (e)?
_____ Greater than _____ Less than _____ Equal to
Justify your answer.
If the ideal voltmeter is replaced by a voltmeter that is not ideal and the experiment is repeated, would the readings of the ideal ammeter be greater than, less than, or equal to those in the data chart before part (c)?
_____ Greater than _____ Less than _____ Equal to
Justify your answer.
[Diagram: Two long vertical conducting rails, separated by horizontal distance, both drawn as vertical lines, oriented into a uniform magnetic field directed into the page (shown by an array of $\times$ symbols filling the region between and around the rails). A resistor of resistance $R$ connects the tops of the two rails (zig-zag resistor symbol labeled $R$). A horizontal conducting bar of mass $M$ and length $L$ (labeled "$M, L$") lies across the rails below the resistor, shown shaded. Point $C$ is marked just above the bar, between the rails. Point $D$ is marked further down between the rails, below the bar's initial position. The left rail is labeled $B$ near its lower end (labeling the magnetic field region). A downward arrow to the right of the figure is labeled "Vertically down," indicating the bar's direction of motion.]
A conducting bar of mass $M$, length $L$, and negligible resistance is connected to two long vertical conducting rails of negligible resistance. The two rails are connected by a resistor of resistance $R$ at the top. The entire apparatus is located in a magnetic field of magnitude $B$ directed into the page, as shown in the figure above. The bar is released from rest and slides without friction down the rails.
What is the direction of the current in the resistor?
_____ Left _____ Right
Is the magnitude of the net magnetic field above the bar at point $C$ greater than, less than, or equal to the magnitude of the net magnetic field before the bar is released?
_____ Greater than _____ Less than _____ Equal to
Justify your answer.
While the bar is above point $D$, is the magnitude of the net magnetic field at point $D$ greater than, less than, or equal to the magnitude of the net magnetic field before the bar is released?
_____ Greater than _____ Less than _____ Equal to
Justify your answer.
Express your answers to parts (c) and (d) in terms of $M$, $L$, $R$, $B$, and physical constants, as appropriate.
Write, but do NOT solve, a differential equation that could be used to determine the velocity of the falling bar as a function of time $t$.
Determine an expression for the terminal velocity $v_T$ of the bar.
Express your answers to parts (e) and (f) in terms of $v_T$, $M$, $L$, $R$, $B$, and physical constants, as appropriate.
Derive an expression for the power dissipated in the resistor when the bar is falling at terminal velocity.
Using your differential equation from part (c), derive an expression for the speed of the falling bar $v(t)$ as a function of time $t$.