Question 1

If 500 J of work are required to carry a 40-C charge from one point to another, the potential difference between these two points is:

Accepted Answer

The potential difference (voltage) between two points is defined as the work done per unit charge to move a charge between those points. Using the formula V = W/Q, where V is the potential difference, W is the work done (500 J), and Q is the charge (40 C), we get V = 500 J / 40 C = 12.5 V.

Question 2

An electron goes from one equipotential surface to another along one of the four paths shown below. Rank the paths according to the work done by the electric field, from least to greatest.

Accepted Answer

D

Question 3

The equipotential surfaces associated with a charged point particle are:

Accepted Answer

The equipotential surfaces for a charged point particle are concentric spheres centered at the particle because the electric field is radial and the potential is proportional to 1/r.

Question 4

Positive charge is distributed uniformly throughout a non-conducting sphere. The highest electric potential occurs:

Accepted Answer

The electric potential due to a uniformly charged non-conducting sphere increases as one moves towards the center from the surface, reaching its maximum value at the center. This is because the potential is directly related to the amount of charge enclosed within a given radius, and all the charge is enclosed at the center.

Question 5

An electron is accelerated from rest through a potential difference V. Its final speed is proportional to:

Accepted Answer

The answer of An electron is accelerated from rest through...

Question 6

The work required to carry a particle with a charge of 6.0-C from a 5.0-V equipotential surface to a 6.0-V equipotential surface and back again to the 5.0-V surface is:

Accepted Answer

Since the particle is only being moved between equipotential surfaces, the electric field remains constant and perpendicular to the direction of motion. Therefore, the work done on the particle is zero, so the answer is A.

Question 7

If the electric field is in the positive x direction and has a magnitude given by E = Cx^2, where C is a constant, then the electric potential is given by V =:

Accepted Answer

The electric potential V is the negative integral of the electric field E with respect to x. Integrating E = Cx^2 gives V = -∫Cx^2 dx = -Cx^3/3.

Question 8

Eight identical spherical raindrops are each at a potential V, relative to the potential far away. They coalesce to make one spherical raindrop whose potential is:

Accepted Answer

The answer of Eight identical spherical raindrops are each at...

Question 9

During a lightning discharge, 30 C of charge move through a potential difference of 1.0 * 10⁸ V in 2.0 * 10^-² s. The energy released by this lightning bolt is:

Accepted Answer

The answer of During a lightning discharge, 30 C of...

Question 10

A hollow conductor is positively charged. A small uncharged metal ball is lowered by a silk thread through a small opening in the top of the conductor and allowed to touch its inner surface. After the ball is removed, it will have:

Accepted Answer

When the small uncharged metal ball touches the inner surface of the positively charged hollow conductor, some of the positive charges from the conductor will flow to the ball, neutralizing it. When the ball is removed, it will have no appreciable charge because the charges that were transferred to it will be evenly distributed over its surface and will cancel each other out.

Question 11

Two large parallel conducting plates are separated by a distance d, placed in a vacuum, and connected to a source of potential difference V. An oxygen ion, with charge 2e, starts from rest on the surface of one plate and accelerates to the other. If e denotes the magnitude of the electron charge, the final kinetic energy of this ion is:

Accepted Answer

The final kinetic energy (K.E.) of the oxygen ion can be calculated using the energy conservation principle. The work done on the ion by the electric field as it moves from one plate to the other is equal to the change in its kinetic energy. Since the ion starts from rest, its initial kinetic energy is 0, and the work done is given by the potential difference (V) times the charge (2e). Therefore, the final kinetic energy of the ion is $K.E. = 2eV$.

Question 12

A particle with mass m and, charge -q is projected with speed v₀ into the region between two parallel plates as shown. The potential difference between the two plates is V and their separation is d. The change in kinetic energy of the particle as it traverses this region is:

Accepted Answer

The answer of A particle with mass m and, charge...

Question 13

An electron moves from point i to point f, in the direction of a uniform electric field. During this placement:

Accepted Answer

The answer of An electron moves from point i to...

Question 14

The electric potential in a certain region of space is given by V = -7.5x² + 3x, where V is in volts and x is in meters. In this region the equipotential surfaces are:

Accepted Answer

The electric potential V given as a function of x alone (-7.5x^2 + 3x) implies that the potential changes with x but is constant with respect to y and z. Therefore, the equipotential surfaces, which are surfaces of constant potential, must be perpendicular to the x-axis and parallel to the yz plane. This makes planes parallel to the yz plane the correct choice.

Question 15

The electric field in a region around the origin is given by  where C is a constant. The equipotential surfaces are:

Accepted Answer

The answer of The electric field in a region around...

Question 16

An electron volt is:

Accepted Answer

An electron volt (eV) is a unit of energy. It is defined as the energy gained or lost by an electron when it moves through a potential difference of 1 volt. Therefore, choice C is the correct answer.

Question 17

An electron has charge -e and mass m_e. A proton has charge e and mass 1840m_e. A "proton volt" is equal to:

Accepted Answer

The answer of An electron has charge -e and mass...

Question 18

A total charge of 7 * 10^-⁸ C is uniformly distributed throughout a non-conducting sphere with a radius of 5 cm. The electric potential at the surface, relative to the potential far away, is about:

Accepted Answer

The electric potential at the surface of a sphere with a uniformly distributed charge can be found using the equation V = kQ/R, where k is Coulomb's constant, Q is the total charge, and R is the radius of the sphere. Plugging in the given values, we get V = (9x10^9)(7x10^-6)/(0.05) = 1.26x10^5 V. To find the potential relative to far away, we need to subtract the potential at infinity, which is 0. Therefore, the answer is 1.3x10^5 V, or B.

Question 19

The potential difference between two points is 100 V. If a particle with a charge of 2 C is transported from one of these points to the other, the magnitude of the work done is:

Accepted Answer

The work done in moving a charge from one point to another is given by the formula w = qV, where w is the work done, q is the charge, and V is the potential difference. Substituting the values given, we get w = (2 C)(100 V) = 200 J. Therefore, the correct choice is A.

Question 20

In separate experiments, four different particles each start from far away with the same speed and impinge directly on a gold nucleus. The masses and charges of the particles are  Rank the particles according to the distance of closest approach to the gold nucleus, from smallest to largest.

Accepted Answer

The distance of closest approach is determined by the particle's momentum, and thus its velocity, as well as the Coulombic attraction between the particle and the gold nucleus. The particle with the highest charge, particle 1, will experience the greatest attraction and thus have the smallest distance of closest approach. The particle with the least charge, particle 4, will experience the weakest attraction and thus have the largest distance of closest approach. However, the question does not provide enough information to determine the distances of closest approach for particles 2 and 3, as their masses and charges are not given. Therefore, particles 1 and 2 must be tied for the second smallest distance of closest approach, followed by particle 3, and then particle 4. Therefore, choice C is the best option.

Quiz 24: Electric Potential

If 500 J of work are required to carry a 40-C charge from one point to another, the potential difference between these two points is:

An electron goes from one equipotential surface to another along one of the four paths shown below. Rank the paths according to the work done by the electric field, from least to greatest.

The equipotential surfaces associated with a charged point particle are:

Positive charge is distributed uniformly throughout a non-conducting sphere. The highest electric potential occurs:

An electron is accelerated from rest through a potential difference V. Its final speed is proportional to:

The work required to carry a particle with a charge of 6.0-C from a 5.0-V equipotential surface to a 6.0-V equipotential surface and back again to the 5.0-V surface is:

If the electric field is in the positive x direction and has a magnitude given by E = Cx2, where C is a constant, then the electric potential is given by V =:

Eight identical spherical raindrops are each at a potential V, relative to the potential far away. They coalesce to make one spherical raindrop whose potential is:

During a lightning discharge, 30 C of charge move through a potential difference of 1.0 * 108 V in 2.0 * 10-2 s. The energy released by this lightning bolt is:

A hollow conductor is positively charged. A small uncharged metal ball is lowered by a silk thread through a small opening in the top of the conductor and allowed to touch its inner surface. After the ball is removed, it will have:

A particle with mass m and, charge -q is projected with speed v0 into the region between two parallel plates as shown. The potential difference between the two plates is V and their separation is d. The change in kinetic energy of the particle as it traverses this region is:

An electron moves from point i to point f, in the direction of a uniform electric field. During this placement:

The electric potential in a certain region of space is given by V = -7.5x2 + 3x, where V is in volts and x is in meters. In this region the equipotential surfaces are:

The electric field in a region around the origin is given by where C is a constant. The equipotential surfaces are: