Physics II Test I
What is the electric field magnitude outside a spherical shell of uniform charge density (sigma) and radius a?
(sigma*a^2)/(E_o*r^2)
Suppose you have two conducting spheres in contact. Sphere 1 has a radius of 30 cm and sphere 2 has a radius of 50 cm. You put 16 ûC of charge on sphere 1. How does the charged end up distributed between the two spheres?
6 ûC on 1 and 10 ûC on 2
An electric charge with charge q is placed in an electric field with field magnitude E. Due to the field, the charge experiences a force F . If the charge is doubled and the field tripled, how much force is then exerted on the charge?
Answer: 6F Solution: The magnitude of the force F on a particle with charge q in an electric field with magnitude E is equal to F = qE.Thus, the new force will be 6F
Two particles each experience a force F . The particles have different masses such that particle 1 has less mass than particle 2, m1 < m2. Compare the magnitude of the accelerations, a1 and a2, of the two particles
Answer: A1>A2 Solution: The heavier particle will experience a smaller acceleration
What is an electrophorus?
Answer: An electrophorus is a flat, conducting plate that develops a large static charge when charged by induction over a dielectric. Solution: An electrophorus is a conducting plate that develops a large electrostatic charge when charged by induction over a charged dielectric.
What is an electroscope?
Answer: An electroscope is a device primarily used for detecting net electric charge Solution: An electroscope is a device for detecting net electric charge
How is the electric flux through a surface related to the number of field lines crossing a surface?
Answer: The number of field lines passing through a surface is proportional to flux through the surface Solution: The electric flux through a surface is proportional to the number of field lines crossing the surface
A negatively charged particle is released from rest in a region of space where it experiences a constant force in the +z direction. Select the choice below that best describes the motion of the particle
Answer: The particle will move in the +z direction with a constantly increasing velocity Solution: The electron will move in the direction of the force and at a constantly increasing speed
The two infinite parallel planes to the right have equalbut opposite uniform charge densities, ±σ. A particle with charge+q is placed between the planes. Rank the magnitude of the totalelectric field due to the two planes and the point charge at thefour points labeled (a) through (d). The points are equidistantfrom the +q particle
Answer: Ea< Eb= Ed< Ec Solution: Parallel Planes Produce Uniform Field: Between the plates: The infinite parallel planes produce a uniformfield. The field of the left plane points to the right of the page as does the field of the right plane. The total field of the two planes points to the right of the page and has the same magnitude at the points a-d Determine the Direction of the Field of the Point Charge: The electric field of the +q charge points radially outward from the charge and has the direction of the force a positive test charge would experience if placed at the point 3 Reason about the Addition of the Vectors: The fields point in the same direction at point (c) and therefore add, so Ec is the largest. The fields are oppositely directed at point (a) and therefore cancel, so Eaisthe smallest. The fields are at right angles at points (b) and and therefore the magnitudes at these points is less than the magnitude at (c)
If two point charges with charge q are spaced an equal distance from the origin on the x-axis on opposite sides of the origin, then the electric force on a particle at the origin is zero. Is this equilibrium stable? If yes why; if no why not?
Answer: No, if the particle is displaced from the origin, then the force tends to push it away from the origin. Solution: The equilibrium is unstable; if a particle at the origin is displaced it feels an outward force and move farther away from the origin.
You are given a negatively charged particle and instructed to determine the direction of the electricfield in a region of space. How can you do this? You may only observe the particle and may not make anyadditional measurements
Answer: Release the particle in the region, it will initially move opposite to the direction of the field Solution: A negative test charge in the presence of an electric field will experience a force opposite the direction of thefield. Objects accelerate in the direction of the force, by Newton's II Law. Thus, the field points in the oppositedirection that the charge moves (assuming it was released from rest)
A uniform volume charge centered at the origin occupies the region r < a. The total charge of the volume charge is Q. If one wished to apply Gauss' law to a spherical Gaussian surface centered at the origin with radius a/2, how is the charge enclosed in the Gaussian surface related to total charge of the volume charge?
Answer: The charge enclosed is less than Q Solution: In configuration (c), the Gaussian surface passes through point P at a distance r from the center of the system.Therefore, A spherical Gaussian surface with outer edge in a volume charge does not enclose the total charge ofthe volume charge. A spherical Gaussian surface with outer edge in a volume charge does not enclose the totalcharge of the volume charge
An electric dipole is placed in an electric field and allowed to rotate about its center. What is the relation between the direction of the electric field lines and the equilibrium orientation of the dipole?
Answer: The dipole is in equilibrium when its moment is parallel to the field line and points in the samedirection as the field line Solution: At equilibrium the dipole moment points in the direction of the field
Select the choice that follows the describes the relation between the electric force on a charged particle and the direction of the electric field lines
Answer: The electric force points either the same direction or in the opposite direction as the field line Solution: The electric force points either the same direction or in the opposite direction as the field line
The figure to the right shows two charged particles:an electron labeled e and a proton labeled p. The two particlesare a distance d apart and the electron is a distance d from thepoint a. What is the direction of the electric field at the point a?
Answer: The electric field points in the positive x direction Solution: The electron is negative. The electric field points toward negatively charged particles, so the electric field due tothe electron at point a points in the +x direction.The proton has a positive charge.The proton and the electronhave charges of equal magnitude. The point a is closer to the electron, so its field is stronger. The total field ata points in the direction of the electron's field in the +x direction
While constructing a leaf electroscope, a student finds the paperclip that connects the bolts to the leaves difficult to work with. To make construction easier, the student uses a plastic tie wrap instead to connect the bolt to the foil leaves. How does this substitution affect the operation of the electroscope?
Answer: The electroscope will cease to function. Solution: Plastic is an insulator, so the electroscope will do nothing.
The Van de Graaff electrostatic generator develops a charge of approximately −1 × 10−5C and a pith ball has charge of approximately 1 × 10−9C. Which of the following describes the relationship between the size of the force the Van de Graaff exerts on the pith ball and the size of the force the pith ball exerts on the Van de Graaff?
Answer: The forces have the same magnitude Solution: Newton's Third Law states that the forces are equal in magnitude and opposite in direction
The earth has a charge of approximately −7 × 105C and a pith ball has a charge of approximately 1 × 10−9C. Which of the following describes the relationship between the size of the force the earth exerts on the pith ball and the size of the force the pith ball exerts on the earth?
Answer: The forces have the same magnitude. Solution: According to Newton's Third Law, the forces will have the same magnitudes and opposite directions.
A metal conducting sphere is grounded as shown to the right. A positively charged object is brought near but does not touch the metal sphere. With the charged object and the metal sphere in the locations drawn at the right with the ground attached, does the metal sphere have a net charge? If so, what is the sign of the net charge?
Answer: The metal sphere has a net negative charge Solution: When the rod is near the neutral conducting sphere, charge separates on the sphere. Since the object is positively charged, a negative charge density is induced on the sphere near the rod, while positive charges are repelled away. If the sphere is grounded while the positive object is near, the separated negative charge is held in place by the rod; the separated positive charge is free to escape to the ground, leaving the sphere with a net negative charge.
A positive charge is moving in the +x direction in a uniform electric field that points in the −x direction. Describe the initial change in speed of the particle
Answer: The particle's speed initially decreases Solution: The force on the particle is in the −x direction because F = qE. The particle initially has velocity in the directionopposite the force on it. This means that the speed of the particle will decrease due to the electric field
A proton (p), a neutron (n), and an electron (e) areshot into a region with a uniform electron field as shown to theright. The field points to the right of the page as drawn. Howdoes the speed of each of these particles change as they travelthrough the field? Treat the particles as point particles
Answer: The speed of the electron decreases, the speed of the proton increases, and the speed of the neutron remains the same Solution: The electron has negative charge. Since the field is to the right, the force on the electron is to the left,~F = q~E. Since the force and velocity are in the opposite direction, the speed will decrease. A proton is positively charged. The direction of the force on the proton is to the right. Since the force and the velocity is in the same direction, the speed increases The neutron has zero charge. The field exerts no force on the neutral particle, so its speed will remain the same
The figure to the right shows two positive point charges along the y axis. A third positive charge is located at the point P on the x axis. In what direction does the electric force on the positive charge at P point?
Answer: Toward the lower right of the page in a direction between the positive x direction and the negative y direction Solution: The force exerted on the charge at point P by the charge at the origin is purely in the x-direction. The force exerted on the charge at point P by the charge located on the +y-axis is directed down and to the right. The sum of these vectors points in the +x- and −y-direction.
The temperature of ocean water and the velocity of the water flow change with the position in theocean. Which of the following quantities are a vector field?
Answer: Water Velocity Solution: Water velocity is a vector, and it can be represented with a vector at each location in the ocean. Therefore, thewater velocity throughout the earth's oceans is a vector field. Water temperature does not have a direction andis therefore not a vector
Can a charged object exert a force on an uncharged insulator? If yes, why; if no, why not?
Answer: Yes, by inducing an electrical polarization in the insulator; the insulator is then attracted to the charged object. Solution: Yes, by inducing an electrical polarization in the insulator; the insulator is then attracted to the charged object. This is the effect that causes a soda bottle to roll toward the charged rod.
A negatively charged rod is brought near a leaf electroscope. While the rod is near the bolt of the electroscope, the leaves are undefelected. The charge of the leaves of the electroscope while the charged rod is near the bolt is
Answer: Zero Solution: Since the leaves are not deflected, they contain zero net charge.
A cylindrical piece of insulating, uncharged material is placed in an external electric field, as shown. The net electric flux passing through the surface of the cylinder is
Answer: Zero Solution: No charge in cylinder so flux is zero. All lines go in and come of out cylinder
Which of the following describes an experiment that demonstrates that there are at least two different types of charge?
Answer: Charge a pair each of glass and rubber rods by rubbing them with felt. Observe that that (1) the glass rods repel each other, (2) the glass rods attract the rubber rods, and (3) the rubber rods repel each other Solution: Certain materials become electrically charged after they are rubbed with other materials. Two rods of similar type, prepared in the same fashion - by rubbing with felt - will repel one another. Two different rods, also prepared in the same fashion, will both repel one another and attract the first two rods. These two distinctive behaviors are the evidence required for determining that there are at least two types of charge.
A farmer claims to have built a machine that manufactures charge. The machine is a huge thing sitting on the ground in the middle of a field and produces 1μC every minute. What can you conclude about the system?
Answer: Charge is being transferred from somewhere else by the device and is not actually created by the device Solution: Charge is absolutely conserved in all processes. If the machine appears to manufacture charge, it must be getting the charge from somewhere. The most likely location is the earth, and so the machine is most probably transferring charge from the earth.
During a process where an object is electrically charged, physically what generally happens to produce the net charge?
Answer: Electrons are transferred from or to the charged object. Solution: They are moved from one place to another.
A particle of mass m is subject to a force F⃗ . What is the acceleration of the particle?
Answer: F⃗/m Solution: The force is related to the acceleration by Newton's Second Law F⃗ = m⃗a. Substituting the Lorentz force and centripetal acceleration gives F_m=[q]vB = ma_c = (mv^2)/r
Two positive point charges are released on a frictionless surface. Which of the following best describes their subsequent motion?
Answer: The particles move apart with a velocity that increases with time. Solution: Coulomb's Law: The magnitude of the electric force between the two particles is F = kq1q2/r^2, and because the two particles have the same sign of charge, the force felt between them is repulsive. Accelerations of the Particles: Newton's second law states F⃗ = m⃗a, so the charges begin to accelerate away from each other due to the electric force felt between them. As they move away from each other, r2 becomes much larger, so the force felt between them becomes much smaller. Since acceleration is directly proportional to force, each particle's acceleration becomes smaller as r approaches infinity. Velocities of the Particles: Even though each particle's acceleration decreases as the distance between the two particles increases, the particles do experience some acceleration even as they move apart. This means that the velocity of each particle continues to increase as the particles move farther apart.
What two elementary particles make up the vast majority of charged matter in the universe?
Answer: protons and electrons Solution: Protons and electrons account for the majority of charged matter in the universe. (Actually, hydrogen - a proton with a single electron - accounts for about 90% of all matter in the universe.)
When two charged ping-pong balls, A and B, are held a small distance apart, which ball is the source of the electric field that acts on ball B?
Ball A
Suppose you spread a certain amount of charge uniformly over a hollow golf tube. Is the electric field inside the tube zero or nonzero (the tube is very long. so answer assuming it is "infinite"
It is zero
A thin, spherical metal shell of radius R carries a uniformly distributed, positive charge Q. In what direction does the electric field inside the shell point?
Neither; the field is zero everywhere inside the shell
The enclosed charge for a closed surface is zero. Does this mean there are no electric field lines crossing the surface?
Not necessarily - a line (or several) could go in and then come out
An electron initially moving horizontally near Earth's surface enters a uniform electric field and is deflected upward. What can you say about the direction of the electron field
The electric field points upward
In the lab experiments, why does the (negative) charged gold tube attract the uncharged soda can?
The negative charge on the tube repels the negative charge in the can and causes it to move away, to the far side of the can, leaving positive charge closer to the tube
