Question 1

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 2

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

B

Question 3

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 is given by:
V = kQ/R
where k is the Coulomb constant (9 x 10^9 N m^2/C^2), Q is the total charge, and R is the radius of the sphere.
Plugging in the given values, we get:
V = (9 x 10^9 N m^2/C^2) * (7 C) / (5 x 10^-2 m)
V = 1.26 x 10^11 V
However, we are asked for the potential relative to the potential far away, which means we need to subtract the potential at infinity (which is 0). Thus, the final answer is:
V = 1.26 x 10^11 V - 0 = 1.26 x 10^11 V = 1.26 x 10^2 MV = 1.3 x 10^2 MV (in scientific notation with appropriate units)
So, the best choice is B.

Question 4

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 5

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 6

An electron volt is:

Accepted Answer

An electron volt (eV) is the energy gained by an electron in moving through a potential difference of 1 volt. It is a unit of energy commonly used in atomic and nuclear physics.

Question 7

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 answer of In separate experiments, four different particles each...

Question 8

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 9

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 10

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

The work done to move a charged particle between two equipotential surfaces does not depend on the path taken, only the potential difference between the surfaces. Since the particle is moving from a 5.0-V surface to a 6.0-V surface and then back to the 5.0-V surface, the net change in potential is zero. Therefore, the work done is also zero.

Question 11

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 12

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 on a charged particle when it is moved through a potential difference is given by:

W= qΔV

Where q is the charge of the particle and ΔV is the potential difference across which it is moved.

Substituting the given values, we get:

W = (2 C)(100 V) = 200 J

Therefore, the magnitude of the work done on the particle is 200 J. The correct choice is A.

Question 13

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

The conductor is positively charged, so electrons will be repelled to the outer surface, leaving the inner surface with a net positive charge. When the small metal ball touches the inner surface, it will become charged by induction but remain uncharged overall. This is because the electrons are attracted to the metal ball, causing them to redistribute themselves to the opposite side of the ball, leaving the side touching the conductor with a net positive charge and the far side with a net negative charge. However, since there is no additional charge added or taken away from the system, the ball will have no overall charge when it is removed from the conductor.

Question 14

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 15

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 16

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 answer of If the electric field is in the...

Question 17

The equipotential surfaces associated with a charged point particle are:

Accepted Answer

The electric field lines of a charged point particle are radially outward from the particle. The equipotential surfaces are perpendicular to the electric field lines, so they are also radially outward and are concentric spheres centered at the particle. Therefore, the best choice is D.

Question 18

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 19

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 20

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

The answer of An electron goes from one equipotential surface...

Quiz 24: Electric Potential

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:

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 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: