Deck 17: Electric Energy and Potential

Question 1

In what direction, relative to the direction of the electric field, does the potential decrease at its maximum rate?

A)in the direction opposite to the electric field
B)depending on the sign of the charge used to measure the potential
C)at right angles to the direction of the electric field
D)in the same direction as the electric field

Answer 1

in the same direction as the electric field

Question 2

At which position between parallel oppositely charged plates is the electric energy of a negative point charge at maximum?

A)at the surface of the positively charged plate
B)halfway between the plates
C)at the surface of the negatively charged plate
D)There is more than one position of maximum energy.

Answer 2

at the surface of the negatively charged plate

Question 3

An electron is near a positive ion. The electron moves toward the ion. Which of these statements is an accurate description of the work done by the ion on the electron?

A)The ion does zero work on the electron.
B)The work that the ion does on the electron is at the expense of the electron's electric potential energy.
C)The work that the ion does on the electron contributes to the electron's increase in electric potential energy.
D)The work that the ion does on the electron does not change the electric potential energy of the electron.

Answer 3

The work that the ion does on the electron is at the expense of the electron's electric potential energy.

Question 4

Identical 2.5 µC charges are located on the vertices of a square with sides that are 1.0 m in length. What is the electric potential (relative to zero at infinity) at the centre of the square?

A)1.3 × 10⁵ V
B)-1.3 × 10⁵ V
C)0.3 × 10⁵ V
D)-0.3 × 10⁵ V

Question 5

A parallel plate capacitor of capacitance C0 has plates of area A with separation b between them. When the capacitor is connected to a battery of voltage ÄV, it has a charge of magnitude Q on its plates. It is then disconnected from the battery and the space between the plates is filled with a material of dielectric constant ê = 3. After the dielectric material is added, what is the potential difference between the plates?

A)ÄV
B)3ÄV
C)2ÄV/3
D)ÄV/3

Question 6

Which of these statements applies to a distribution of charges located in a finite region of space?

A)Electric potential is zero at the origin.
B)Electric potential is zero at infinity.
C)Electric potential is infinite at the origin.
D)The location where electric potential is zero may be chosen arbitrarily.

Question 7

Six equal negative point charges, -q, are placed symmetrically around a circle of radius R. What is the electric potential at the centre of the circle?

A)[0]
B)[-3q/(2ðå₀R)]
C)[+q/(4ðå₀R)]
D)[-q/(2ðå₀R)]

Question 8

By what mechanism are Na and Cl ions separated when rock salt is dissolved in water?

A)by formation of a hydration shell that prevents a neutralizing electron exchange
B)by attachment of an electron from Na to the positive end, and the positive Na ion to the negative end of the same water molecule
C)by attachment of an electron from Cl to the positive end, and the positive Cl ion to the negative end of the same water molecule
D)by neutralization of the ions by electron exchange with the water molecule

Question 9

One negative and two positive charges, each of magnitude 3 ìC, are at the vertices of an equilateral triangle of side 50.0 cm. What is the potential (relative to zero at infinity) at the mid-point between the two positive charges?

A)1.3 × 10⁶ V
B)1.5 × 10⁵ V
C)1.2 × 10⁵ V
D)7.5 × 10⁴ V

Question 10

The potential energy at which neutralization occurs for atoms X and Y in a diatomic salt corresponds to the ions X⁺ and Y^- being 0.7 nm apart. What is the value, in kJ/mol, of the change in internal energy required for this to occur?

A)94 kJ/mol
B)198 kJ/mol
C)250 kJ/mol
D)350 kJ/mol

Question 11

What is the change in the electric potential energy (in electron volts) of a singly charged positive ion, located at a point 10 nm from a water molecule, when the dipole of the water molecule rotates from pointing toward the ion to pointing at right angles to it?

A)-6 × 10^-4 eV
B)6 × 10^-4 eV
C)-10^-3 eV
D)10^-3 eV

Question 12

In the Bohr model of the hydrogen atom, the electron circles the proton at a distance of 0.51 × 10^-10 m. What is the potential at the position of the electron?

A)-14.12 V
B)14.1 V
C)-28.24 V
D)28.24 V

Question 13

A uniform electric field of magnitude 150 V/m is directed in the positive x-direction. A +12.0 ìC charge moves from the origin to the point (x, y) = (20.0 cm, 25.0 cm). Through what potential difference does the charge move?

A)5.8 × 10^-4 J
B)4.5 × 10^-4 J
C)3.6 × 10^-4 J
D)2.9 × 10^-4 J

Question 14

The potential across a cell membrane of thickness 0.5 ìm increases by 75 mV from inside to outside. What is the surface charge density on the outside surface of the membrane?

A)1.5 ìC/m²
B)-1.5 ìC/m²
C)0.8 ìC/m²
D)-0.8 ìC/m²

Question 15

Which of the following defines the electric potential field at a given point?

A)the potential energy of a unit probe charge located at that point
B)the potential energy of a unit positive probe charge located at that point
C)the potential energy of a any charge at that point
D)the negative of the potential energy of a unit charge at that point

Question 16

How much energy is stored in a 10 µF capacitor when ÄV = 25 V?

A)3 × 10^-4 J
B)2 × 10^-3 J
C)3 × 10^-3 J
D)6 × 10^-3 J

Question 17

A nerve cell fires with a frequency of 50 Hz. With each firing, 10⁵ singly charged potassium ions are ejected through the cell's membrane, across which exists a potential of 90 mV. At what rate must energy be supplied to the nerve cell in order for it to fire?

A)7 × 10^-15 W
B)3 × 10^-14 W
C)8 × 10^-14 W
D)9 × 10^-13 W

Question 18

To recharge a 12 V battery, a battery charger must move 4.4 × 10⁵ C of charge from the negative to the positive terminal. What amount of work is done by the battery charger?

A)-5.3 × 10⁶ J
B)2.6 × 10⁵ J
C)5.3 × 10⁵ J
D)5.3 × 10⁶ J

Question 19

A charge of 1 ìC is spread uniformly around a ring of radius 10 cm. What is the potential at a point located 5 cm from the centre, along the axis of the ring?

A)80 kV
B)-80 kV
C)16 kV
D)-16 kV

Question 20

An initially uncharged parallel plate capacitor is charged by a battery. The battery is then disconnected. Which of these statements applies at that point?

A)There is no charge on either plate of the capacitor.
B)The magnitude of the electric field outside the space between the plates is approximately zero.
C)The capacitance now increases when the distance between the plates increases.
D)The capacitor can be discharged by grounding either of its two plates.

Question 21

The energy stored in a capacitor is proportional to the square of the amount of charge on each plate.

Question 22

If you were required to build a capacitor that was both small and had a high capacitance, what factors would you need to consider in its design?

Question 23

In the classical model of an atom, a positively charged nucleus is surrounded by a "cloud" of electrons that may be regarded as a spherically symmetric, uniform distribution of charge. Describe what happens when an external electric field is applied to the atom.

Question 24

When a dielectric material is inserted into an air-spaced capacitor that has been charged, a voltmeter connected across the plates of the capacitor will show an increase in voltage.

Question 25

The energy stored in a capacitor is proportional to the electric field strength between the plates.

Question 26

Explain why working with electric potentials is generally much easier than working with electric fields.

Question 27

The Bohr model of the hydrogen atom states that the single electron can exist only in certain permitted orbits around the proton. The radius of each Bohr orbit is r = n²(0.051 nm), where n = 1, 2, 3,…. Calculate the change in electric potential energy of a hydrogen atom when the electron makes a transition from the n = 2 to the n = 1 orbit. Express your answer in electron volts.

Question 28

An electron is in a close proximity to a negative ion. The electron moves away with kinetic energy that comes from conversion of electric potential energy of an electron near a negative ion.

Question 29

A free electron and a proton are released from rest halfway between a pair of oppositely charged parallel plates. The proton, being the heavier particle, will reach the negative plate before the electron reaches the positive plate.

Question 30

The points on the surface of a sphere centred on a point charge form an equipotential.

Question 31

If a charged particle moves along a path for which its displacement at each point is perpendicular to the electric field at that point, then its potential energy remains constant on that path.

Question 32

The change in potential energy of a particle in an electric field is the negative of the work done by an external force on displacing the particle.

Question 33

The amount of charge stored on the plates of a capacitor connected to a fixed voltage source, such as a battery, increases when the separation of the plates is decreased.

Question 34

What property of a defibrillator contributes most to improving the survival probability of a cardiac patient?

A)a large enough capacitor
B)short time delay for charging the capacitor with sufficient charge
C)enough batteries to create a large electric potential across the capacitor
D)a long retention time for charge on the plates of the capacitor

Question 35

In the old cathode ray tubes, the light on the screen is produced by electrons striking the screen at high velocity. Describe how this high velocity may be achieved.

Question 36

Describe the path of an electron injected horizontally into a region of uniform electric field with a direction that is vertically upward.

Question 37

A voltmeter measures potential.

Question 38

We treat an unknown biological membrane as a parallel plate capacitor with a dielectric material between its plates. You know the capacitance per unit area in unit F/m². You can determine the dielectric constant of the membrane material without the need for an additional parameter.

Question 39

Regarding Earth and a cloud layer 1000 m above Earth as the "plates" of a capacitor, calculate the capacitance if the cloud layer has an area of 1.0 km². If an electric field of 2.0 × 10⁶ V makes the air break down and conduct electricity (lightning), what is the maximum charge the cloud can hold?

Question 40

The potential in the field of a dipole is at its maximum along the dipole axis.

Question 41

How would you expect the dielectric constant of a material to depend on the dipole moment of the constituent molecules?

Question 42

The plates of a charged capacitor attract each other due to the electric forces between them. Suppose the capacitor is disconnected from the battery used to charge it, so the amount of charge on each plate is fixed. An external force is applied to increase the separation of the plates. Where is the additional energy required for this process being stored?

Question 43

For a resting nerve, when no impulse is passing through, determine the dielectric constant k of a nerve membrane, taking capacitance per unit area of a membrane to be 0.01 F/m², and the width of the membrane (the distance between positive and negative plates) to be y = 6 nm.

Question 44

For any form of energy, the energy density over a region is defined as the amount of energy in the region divided by the volume of the region. Consider the case of a charged capacitor, so that an electric field exists between the plates. Calculate the energy density, and show that it is independent of the geometry of the capacitor. What generalization might one draw from this?

Question 45

Calculate the value of the electric field across a human nerve membrane. The value of potential difference is 70 mV, and the width of the membrane (the distance between positive and negative plates) is 6 nm.