AP Physics C: Electricity and Magnetism Full-length practice exam 3

A uniformly charged thin ring of radius $R$ and total charge $Q$ lies in the $xy$-plane centered at the origin. The electric field on the axis of the ring at distance $z$ from the center points:

A toroid has $N$ turns, inner radius $a$, outer radius $b$, and carries current $I$. Using Ampère's law with a circular Amperean loop of radius $r$ ($a<r<b$), the magnetic field inside the toroid is:

Lenz's law states that the direction of the induced current in a loop is such that:

Two capacitors $C_1=4\mu \text{F}$ (initially charged to $V_1=12\text{V}$) and $C_2=8\mu \text{F}$ (initially uncharged) are connected in parallel by closing a switch. The final common voltage and the energy dissipated in the connecting wires are:

In a circuit with two parallel resistors $R_1=6\Omega$ and $R_2=3\Omega$ in series with $R_3=4\Omega$, connected to a $12\text{V}$ ideal battery, the voltage across the parallel combination is:

A coaxial cylindrical capacitor has inner radius $a$, outer radius $b$, and length $L$. The capacitance per unit length is:

An infinitely long line charge has linear charge density $\lambda >0$. Using Gauss's law with a coaxial cylindrical Gaussian surface of radius $r$ and length $L$, the electric field at distance $r$ from the line is:

Two point charges $q_1=+3\mu \text{C}$ and $q_2=-3\mu \text{C}$ are separated by $r=0.30\text{m}$. Using $k=9\times 10^9{\text{N⋅m}}^2/{\text{C}}^2$, the magnitude of the electric force between them is:

The electric potential at a distance $r$ from the center of a uniformly charged insulating sphere of radius $R$ and total charge $Q$, for $r<R$, is:

A conductor in electrostatic equilibrium has which of the following properties?

A proton ($m_p=1.67\times 10^{-27}\text{kg}$, $q=1.60\times 10^{-19}\text{C}$) moving with speed $v=2.0\times 10^6\text{m/s}$ enters a region with both $E$ and $B$ fields. For the proton to travel in a straight line (velocity selector), with $v=v\hat{x}$, $B=B\hat{z}=0.050\text{T}\hat{z}$, the required electric field $E$ and its magnitude are:

A resistor $R=50\Omega$ dissipates power $P=8\text{W}$. The current through it and the voltage across it are:

A solid insulating sphere of radius $R$ carries uniform volume charge density $\rho$. For a point inside the sphere at radius $r<R$, Gauss's law gives the electric field magnitude:

A rectangular loop of area $A=0.04{\text{m}}^2$ is in a uniform magnetic field $B$ that increases at rate $dB/dt=50\text{T/s}$. The magnitude of the induced EMF in the loop is:

An RC circuit with $R=1\text{k}\Omega$ and $C=10\mu \text{F}$ is driven by a square-wave voltage that steps from $0$ to $V_0=10\text{V}$ at $t=0$ (with $C$ initially uncharged). The voltage across the capacitor at $t=2\tau$ (where $\tau =RC$) is:

A particle of mass $m$, charge $q$, enters a uniform magnetic field $B$ perpendicular to its velocity $v$. The radius of the circular orbit is:

A parallel-plate capacitor with plate area $A=0.10{\text{m}}^2$ and gap $d=2\text{mm}$ is filled with a dielectric of $\kappa =5$. A voltage $V=100\text{V}$ is applied. The surface charge density ${\sigma }_f$ on the capacitor plates (free charge) is:

Two large parallel conducting plates separated by distance $d$ each carry surface charge density $+\sigma$ and $-\sigma$ respectively. A small conducting sphere of radius $a\ll d$ with net charge $q$ is held midway between the plates. Ignoring image charges, the electric force on the sphere is:

The energy stored in an inductor of inductance $L=50\text{mH}$ carrying current $I=4\text{A}$ is:

A capacitor $C=10\mu \text{F}$ is charged by a battery $V=100\text{V}$ and then disconnected. The plates are then pulled apart from separation $d$ to separation $2d$. Which of the following correctly describes the new voltage across the capacitor?

In the Wheatstone bridge circuit, resistors $R_1$ (top-left) and $R_2$ (top-right) form one pair of arms; $R_3$ (bottom-left) and $R_X$ (bottom-right) form the other. A galvanometer connects the midpoints. The bridge is balanced when:

Three capacitors $C_1=6\mu \text{F}$, $C_2=3\mu \text{F}$, and $C_3=2\mu \text{F}$ are connected in series across a $12\text{V}$ battery. The total energy stored in the combination is:

A long straight wire carries current $I=5\text{A}$. The magnetic field at a perpendicular distance $r=0.10\text{m}$ from the wire has magnitude (using ${\mu }_0=4\pi \times 10^{-7}\text{T⋅m/A}$):

An LC circuit consists of an inductor $L=0.10\text{H}$ and capacitor $C=100\mu \text{F}$. The capacitor is initially charged to $V_0=10\text{V}$ and the switch is closed at $t=0$. The angular frequency of oscillation $\omega$ and the maximum current $I_{\max }$ are:

An infinite plane of charge has surface charge density $\sigma$. Using Gauss's law with a pillbox Gaussian surface that straddles the sheet, the electric field magnitude on each side of the sheet is:

The electric potential in a region is $V(x,y)=3x^{2}y-y^3$ (in volts, with $x,y$ in meters). The $x$-component of the electric field at the point $(1,1)$ is:

A Hall-effect sensor: a flat conductor (width $w$, thickness $t$) carries current $I$ in the $+x$ direction in a field $B=B\hat{z}$. Charge carriers are electrons (charge $-e$, number density $n$). At steady state, the magnitude of the Hall voltage across width $w$ is:

An RC circuit has $R=10\text{k}\Omega$, $C=20\mu \text{F}$, and battery $V_0=6\text{V}$. The switch is closed at $t=0$ with $C$ initially uncharged. The energy dissipated in the resistor from $t=0$ to $t\to \infty$ is:

A solenoid of $N=500$ turns, length $\ell =0.25\text{m}$, and cross-sectional area $A=2.0\times 10^{-4}{\text{m}}^2$ carries current $I$. The self-inductance of the solenoid is:

A solid insulating cylinder of radius $R$ and infinite length has non-uniform volume charge density $\rho (r)={\rho }_{0}r/R$, where $r$ is the distance from the axis. Using Gauss's law, the electric field magnitude for $r<R$ is:

An ammeter has negligible resistance. A voltmeter has very high resistance. Which connection correctly measures the voltage across resistor $R_2$ in a series circuit containing $R_1$ and $R_2$?

Three resistors $R_1=2\Omega$, $R_2=3\Omega$, $R_3=6\Omega$ are connected in parallel across a $12\text{V}$ source. The total power delivered by the source is:

Using Kirchhoff's current law at a node, if currents $I_1=3\text{A}$ and $I_2=5\text{A}$ flow into the node, and $I_3$ flows out, which of the following is the correct application of KCL?

Using Ampère's law, the magnetic field at a distance $r$ inside a long cylindrical conductor of radius $R$ carrying a total current $I$ uniformly distributed over its cross section is:

A capacitor of capacitance $C$ is fully charged to voltage $V_0$ and then disconnected from the battery. A dielectric of dielectric constant $\kappa$ is then inserted, filling the gap completely. What happens to the stored energy?