U2 MCQ Practice - AP E&M

A charge +𝑄 is inside a hollow region in an electrically neutral piece of solid metal, as shown. The dashed line represents a Gaussian surface within the metal that completely encloses the hollow region.

At which of the three labeled points is the electric field equal to zero?

• X only

• Y only

• X and Z only

• Y and Z only

• X, Y, and Z

A negatively charged rod is brought close to, but does not touch, an isolated, neutral conducting sphere. The sphere is then grounded. The ground is then removed, and the rod pulled away from the sphere. Which of the following correctly states the new charge on the sphere and provides an accurate statement of reasoning to support this claim?

• The sphere becomes positively charged, because negative charges move from the sphere to the ground.

• The sphere becomes positively charged, because positive charges move from ground to the sphere.

• The sphere becomes negatively charged, because positive charges move from the sphere to the ground.

• The sphere becomes negatively charged, because negative charges move from ground to the sphere.

• The sphere remains neutral, because it was grounded during the charging process.

Conducting spheres 1 and 2 on insulating stands have radii 2R and R, respectively. The spheres are very far apart. Sphere 1 has an initial net charge +Q and Sphere 2 is initially neutral. The spheres are then connected by a conducting wire, as shown. The wire is then removed. Which of the following represents the value of the net charge on Sphere 1 after the wire is removed?

• Q/2

• 2Q/3

• 3Q/4

• 4Q/5

• Q

A parallel plate capacitor is connected to an ideal battery of voltage V, as shown in the figure. The capacitor is allowed to become fully charged to a maximum charge Q. If the plates of the capacitor are moved to twice their original separation, the maximum charge stored on the capacitor plates is Q'. Which of the following gives the correct ratio for Q'/Q?

• 1/4

• 1/2

• 1

• 2

• 4

An experiment is performed using a parallel plate capacitor and a voltmeter. The purpose of the experiment is to determine a value for the permittivity constant epsilon0. The capacitor is fully charged and then placed in the circuit shown, where the voltmeter can be used to measure the potential difference across the plates. Measurements for the potential difference are made as the distance d between the plates is increased, and the data are shown in the graph. According to the equation C=(epsilon0*A)/d, the graph should be linear. This is true for small values of d, but for larger values the graph diverges from the straight line. Which of the following is a plausible source of error that may have caused the nonlinear result?

• Measuring the voltage causes the capacitor to gain charge from the voltmeter’s battery.

• As the distance between the plates increases, the effective value of the dielectric constant of air becomes greater than 1.

• As the distance between the plates increases, the effective area of the plates increases.

• The resistance of the capacitor increases, which causes the reading from the voltmeter to decrease.

• As the distance between the plates increases, edge effects come into play and the electric field between the plates is no longer constant.

A circuit consisting of a capacitor connected to an ideal battery is shown above. The capacitor is allowed to become fully charged to a maximum charge Q. The potential difference across the plates of the capacitor is V, and the energy stored in the capacitor is U . The plates are moved closer together, as shown in the figure, until the plates are a distance d/2 apart. What is the new potential difference across the plates and the new energy stored in the capacitor?

• V ; U

• V ; 2U

• V ; 4U

• 2V ; 2U

• 2V ; 4U

A parallel plate capacitor with air between the plates is charged and then disconnected from the source of emf. If the space between the plates is now filled with a dielectric, what happens to the capacitance of the capacitor and the magnitude of the electric field between the plates?

• C increases ; E magnitude increases

• C increases ; E remains constant

• C increases ; E decreases

• C decreases ; E magnitude increases

• C decreases ; E magnitude decreases

A 3.5 microFarad capacitor is connected to a 12⁢ V battery and allowed to fully charge. The capacitor is then isolated from the battery, and a material with a dielectric constant of 3 is inserted between the plates. Which of the following is the change in potential difference across the plates of the capacitor as the dielectric is inserted?

• 0

• 4V

• 6V

• 8V

• 24V

Two identical capacitors, X and Y, are connected in series across a battery. A dielectric material with 𝜿 = 5 is placed in capacitor X. Once equilibrium is reached, how do the potential differences across the two capacitors and their charges compare?

• Vx > Vy ;

  Qx > Qy

• Vx > Vy ;

  Qx = Qy

• Vx = Vy ;

  Qx > Qy

• Vx < Vy ;

  Qx = Qy

• Vx < Vy ;

  Qx < Qy

A conducting plate and a conducting cylinder are connected to a battery, as shown above. Which of the following best represents the electric field between the two objects?

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