Unit 2 Progress Check - MCQ

Unit 2 Progress Check: MCQ An isolated conducting sphere of radius is initially uncharged. A point charge is placed a distance from the center of the sphere, as shown in the figure. Points 1 and 2 are points on the surface of the sphere such that the point charge and points 1, 2, and all fall on the same line. 1. The electric field at point due to the point charge and the sphere is (A) zero (B) (C) (D) (E) 2. Which of the following is a correct for the potential difference between the electric potentials at points 1 and 2 on the surface of the sphere and gives evidence to support this claim? (A) , because the surface of the sphere is an equipotential surface. (B) , because both points are the same distance from the center of the sphere. (C) , because an excess charge of magnitude (D) , because both points are the same distance from the center of the sphere. is induced on the surface of the sphere. (E) , because an excess charge of magnitude is induced on the surface of the sphere. A positively charged conducting spherical shell of radius is a distance away from a second positively charged conducting spherical shell of radius , where . The two shells are connected by a thin metal wire, and the equilibrium is established. At equilibrium, the small shell carries a charge and the large shell carries a charge , as shown. 3. Which of the following is a correct equation relating the radii of the shells and the charges on the shells? (A) (B) (C) (D) (E) 4. Points , , and in the vicinity of the shells are shown in the figure. Points and are just outside the surface of each sphere, and point is equidistant from both spheres. Which of the following indicates the point at which the magnitude of the electric field is greatest and supplies evidence for the claim? (A) Point , because is less than . (B) Point , because is less than . (C) Point , because the electric field from each sphere adds together at (D) Point , because is greater than . (E) Point , because is greater than . . In an experiment to investigate the properties of a capacitor, students connect a parallel plate capacitor to a variable voltage source as shown. 5. To determine how the electric field between the plates of the capacitor changes as the potential difference across the plates changes, the students set up an electron emitter as shown to send a beam of electrons between the plates of the capacitor. When the voltage is turned on, it is observed that the beam is deflected upward. As the voltage is increased, the electrons are deflected more. Which of the following statements is supported by this observation? (A) The electric field between the plates is directed downward, and its strength increases with increasing voltage. (B) The electric field between the plates is directed upward, and its strength increases with increasing voltage. (C) The electric field between the plates is directed upward, and its strength decreases with increasing voltage. (D) The electric field between the plates is directed downward, and its strength decreases with increasing voltage. (E) The electric field is initially directed upward but changes direction with increasing voltage. 6. Without using the electron emitter, the variable voltage source is set at a fixed value, and the spacing between the plates is gradually increased without disconnecting the capacitor from the voltage source. Which of the following is a correct claim about how this will affect the charge on the plates of the capacitor and provides evidence to support this claim? (A) The charge on the plates of the capacitor will increase, because the capacitance increases. (B) The charge on the plates of the capacitor will decrease, because the capacitance increases. (C) The charge on the plates of the capacitor will increase, because the capacitance decreases. (D) The charge on the plates of the capacitor will decrease, because the capacitance decreases. (E) The charge on the plates of the capacitor will not change, because the voltage remains the same. An uncharged parallel-plate capacitor is connected through an open switch to a battery of voltage and the capacitor is allowed to charge. . The switch is closed 7. The charge on the capacitor is measured at various times while it is charging. The data yield the graph shown. Which of the following could be determined using values obtained from the graph? (A) The capacitance of the capacitor (B) The area of the capacitor’s plates (C) The separation between the capacitor’s plates (D) Whether a dielectric has been placed between the capacitor’s plates (E) No values without knowing the initial current in the circuit 8. As the capacitor is charged, energy is transferred to it from the battery. When the capacitor is fully charged, the energy stored in the capacitor is . The energy stored in the capacitor when the stored charge is is (A) (B) (C) (D) (E) 9. Two isolated spheres, each of radius , are shown. Both spheres carry charge . One sphere is metal and one is plastic. No other electric fields are present. Which of the following accurately describes the spheres? The charge on the metal sphere may be distributed evenly throughout the sphere. The charge on the plastic sphere may be distributed evenly throughout the sphere. The surface of the metal sphere must be an equipotential surface. The surface of the plastic sphere must be an equipotential surface. (A) only (B) and (C) and (D) , (E) , only only , and , , and only 10. The figure shows an uncharged conducting cubic shell and a positive point charge outside the shell. There are two lettered points and inside the shell where the electric field can be measured. The electric field at points and are and , respectively. Point is at the center of the cubic shell. Outside the shell are points and where the charge can be placed. All four points are along the same line. Which of the following statements is correct? (A) If the point charge is placed at point , . (B) If the point charge is placed at point , . (C) If the point charge is placed at point , . (D) If the point charge is placed at point , . (E) If the point charge is placed at point , . 11. An infinitely long, thin, nonconducting rod carrying charge is placed inside an infinitely long metal cylinder that has no net charge. The cylinder is not grounded, and the rod does not touch the cylinder. Which of the following describes the distribution of charges on the cylinder? (A) The inside surface of the cylinder has a charge of , and the outside surface has a charge of because the electric field outside the metal cylinder must be zero. , (B) The inside surface of the cylinder has a charge of , and the outside surface has a charge of because the electric field inside the metal cylinder must be zero. , (C) The inside surface of the cylinder has a charge of , and the outside surface has no charge, because the electric field outside the metal cylinder must be zero. (D) The inside surface of the cylinder has a charge of , and the outside surface has no charge, because the electric field inside the metal cylinder must be zero. (E) There is no net charge on either surface of the cylinder, because the electric field outside the metal cylinder must be zero. 12. A positive test charge is brought near to, but not touching, a conducting sphere that is connected to the ground. Both objects remain at rest in the positions shown above. Charge begins to flow from the ground to the sphere. Which of the following statements best describes when charge stops flowing, and provides justification for the claim? Charge will flow until the electric field at the surface of the sphere is equivalent to the electric field of (A) the test charge, because then the excess charge on the surface of the sphere will be equal to the charge of the test charge. (B) Charge will flow until the electric field at the surface of the sphere is equivalent to the electric field of the test charge, because then the net force on all charges on the surface of the sphere will be zero. (C) Charge will flow until the potential at the surface of the sphere is the same as the potential of the test charge, because then the net force on all charges on the surface of the sphere will be zero. Charge will flow from the ground to the sphere until the potential is the same everywhere within the (D) sphere, because then the excess charge on the surface of the sphere will be equal to the charge of the test charge. (E) Charge will flow from the ground to the sphere until the potential is the same everywhere within the sphere, because then the net force on all charges on the surface of the sphere will be zero. 13. The parallel plate capacitor represented above was used by students in an experiment. The electric potential is set to zero at plate , and the electric potential at the other positions is measured. The distance between the difference positions is also measure, and the data are shown in the table. Based on the data provided, which of the following gives the correct magnitude and direction of the electric field inside the plates of the capacitor? Electrical Potential (A) to the left (B) to the right (C) to the left (D) to the right Distances (E) The magnitude of the electric field increases in value from 14. to and is directed to the right. Students design an experiment to test the effect of changing the plate area on the capacitance of a parallel plate capacitor. They use two sheets of aluminum foil and separate them with foam. They measure the capacitance of the capacitor and then begin to reduce the areas of the foil plates. Which of the following graphs would reasonably show the capacitance as a function of area for their data? (A) (B) (C) (D) (E) 15. In an experiment, students study the variation of the capacitance of a parallel plate capacitor as the distance between the plates is changed. The students connect the capacitor to a battery and make measurements of , the charge stored on the capacitor, and potential difference across the plates of the capacitor. In an attempt to confirm the equations and , students construct a graph of as a function of , expecting a straight line trend for the data, but the data are significantly nonlinear. Which of the following could be one potential source of error? (A) The battery has significant internal resistance. (B) The wires have significant resistance. (C) The electric field between the plates of the capacitor becomes significantly nonuniform as the value of increases. (D) Electric current starts to leak between the plates as they are pulled farther apart. (E) Linear data require a graph as a function of . 16. A capacitor is connected to a battery as shown above. The plates of the capacitor are pulled apart using insulating handles while the capacitor remains connected to the battery. Will the capacitance and energy stored in the capacitor increase, decrease, or remain the same? Capacitance Energy Stored (A) Increase Capacitance Increase Energy Stored (B) Increase Capacitance Remain the same Energy Stored (C) Remain the same Capacitance Decrease Energy Stored (D) Decrease Capacitance Decrease Energy Stored (E) Decrease 17. Remain the same A parallel-plate capacitor of capacitance has plate area , and the plates are a distance apart. The capacitor is connected to a battery of voltage . When fully charged, the capacitor stores a charge . Which of the following claims is true? (A) Connecting the capacitor to a battery of voltage will increase the capacitance of the capacitor to . (B) Connecting the capacitor to a battery of voltage will increase the capacitance of the capacitor to . (C) Increasing the area of the plates to will decrease the capacitance of the capacitor to (D) Increasing the area of the plates to will increase the capacitance of the capacitor to (E) Increasing the charge stored on the capacitor to 18. . . will increase the capacitance of the capacitor to . A parallel-plate capacitor has capacitance . Which of the following is a modification, with correct reasoning, that will decrease the capacitance of the capacitor to ? (A) Insert a dielectric slab between the plates, because then charges can flow more easily between the plates. 19. (B) Decrease the separation between the plates by a factor of two, because then less work will be necessary to get charges from one plate to the other. (C) Decrease the area of the plates by a factor of two, because then half as much charge will deposit on the plates when the same potential difference is applied. (D) Decrease both the area of the plates and the separation between them by a factor of two, because then the capacitor will be smaller. (E) Decrease both the area of the plates and the separation between them by a factor of two, because then the charge density on the plates will be smaller. A parallel plate capacitor is charged by connecting it to a battery. After the steady state is reached, the electric energy stored in the capacitor is . Which of the following makes a correct claim about the amount of work needed to charge the capacitor and gives evidence to support this claim? (A) No work is needed to charge the capacitor, because the charges will naturally move to their equilibrium position. (B) The amount of work needed to charge the capacitor is , because in all physical situations, the work done is equal to the final potential energy of the system. The amount of work needed to charge the capacitor is , because, when integrating the equation with the correct limits yields the equation for the energy stored on a capacitor, (C) . The amount of work needed to charge the capacitor is , because it takes (D) charges from the battery and to place the charges on the capacitor. (E) 20. 21. The amount of work needed to charge the capacitor is for the battery . of work to remove the , because for a capacitor while A capacitor is connected to an ideal battery, and the capacitor is allowed to charge completely. The capacitor is then isolated from the battery, and a material with a dielectric constant of is slowly inserted between the plates of the capacitor. Which of the following correctly describes the process of inserting the material? (A) A force is required to push the material into the space between the plates, and the potential energy stored between the plates of the capacitor will remain the same. (B) A force is required to push the material into the space between the plates, and the potential energy stored between the plates of the capacitor will increase by a factor of . (C) A force is required to push the material into the space between the plates, and the potential energy stored between the plates of the capacitor will increase by a factor of . (D) The capacitor will pull the material into the space between the plates, and the potential energy stored between the plates of the capacitor will decrease by a factor of . (E) The capacitor will pull the material into the space between the plates, and the potential energy stored between the plates of the capacitor will decrease by a factor of . An isolated parallel plate capacitor is constructed with a removable piece of dielectric material between two parallel conducting plates. Which of the following correctly predicts the effect inserting the dielectric material will have on the capacitance of the capacitor and the magnitude of the electric field between the plates of the capacitor? (A) The capacitance will increase, and the magnitude of the electric field will decrease. (B) The capacitance will increase, and the magnitude of the electric field will increase. (C) The capacitance will decrease, and the magnitude of the electric field will decrease. (D) The capacitance will decrease, and the magnitude of the electric field will remain the same. (E) The capacitance will decrease, and the magnitude of the electric field will increase. 22. An air-filled parallel-plate capacitor of capacitance is connected to a battery of voltage . When fully charged, the capacitor stores a charge and the electric field between the plates is . While the capacitor is connected to the battery, a material with a dielectric constant is inserted into the space between the plates of the capacitor. As a result, the magnitudes of the charge stored on the capacitor and the electric field between the plates are Charge Stored Electric Field Charge Stored Electric Field Charge Stored Electric Field Charge Stored Electric Field Charge Stored Electric Field (A) (B) (C) (D) (E) 23. An isolated parallel-plate capacitor with plate spacing of has capacitance when it has a dielectric constant . The plate separation is increased to , and the dielectric is replaced with material of dielectric constant . The new capacitance of the capacitor is (A) (B) (C) (D) (E) 24. A parallel plate capacitor with plate area and plate separation has a material between its plates with dielectric constant . When this capacitor is isolated and fully charged, the energy stored in the capacitor is . The material is slowly removed from between the plates. After the material is removed, the energy stored in the capacitor is (A) (B) (C) (D) (E) 25. An air-filled capacitor is connected to a -volt battery. While keeping the capacitor connected to the battery, a material with dielectric constant is inserted between the plates. The increase in the energy stored on the capacitor by inserting the material is most nearly (A) (B) (C) (D) (E) 26. A capacitor with a dielectric of constant is fully charged and then isolated. The dielectric is then removed from the capacitor. Which of the following claims about removing the dielectric from the isolated capacitor is correct? (A) The energy stored in the capacitor remains unchanged. (B) The energy stored in the capacitor increases by a factor of . (C) The energy stored in the capacitor increases by a factor of . (D) The capacitance of the capacitor remains unchanged. (E) The capacitance of the capacitor increases by a factor of . 27. A parallel plate capacitor with air between its plates is connected to a battery and fully charged. While keeping the charged capacitor connected to the battery, a dielectric material is introduced between the plates. Which of the following is a true statement about how adding the dielectric affects to the capacitor? (A) The charge stored on the capacitor will increase. (B) The charge stored on the capacitor will decrease. (C) The electric field between the plates will increase. (D) The electric field between the plates will decrease. (E) The effect cannot be determined without knowing the dielectric constant material. 28. In an experiment, students connect a capacitor to a battery of constant voltage . Different material of dielectric constant can be inserted between the plates as shown. The dielectric constants for three materials that will be inserted between the plates are , , and . Which of the following sets of data of the final charge on the capacitor for each dielectric material supports the claim that ? (A) (B) (C) (D) (E) 29. In an experiment, students connect a parallel plate capacitor with square conducting plates of side length to a battery of potential difference . A dielectric slab of constant with square faces of side length is slowly inserted between the plates at short intervals of distance, pausing at each interval so that the capacitor reaches a steady state. The students measure the charge stored on the capacitor each time steady state is reached. The process is repeated until the dielectric is completely inside the capacitor. The students use the data to create a graph of the charge stored on the capacitor as a function of the distance that the dielectric has been inserted into the capacitor. Which of the graphs correctly represents the data collected from the experiment? (A) (B) (C) (D) (E) 30. Students perform an experiment using a circuit that contains two parallel plate capacitors. Capacitor is fully charged and connected to initially uncharged capacitor , as shown in the circuit. Which of the following is a correct hypothesis by the students regarding the relative magnitude of the potential difference and across the plates of capacitors and , respectively, when the circuit reaches steady state? (A) (B) (C) (D) (E)