Relationships Between Force, Field, Energy, Potential

What is the potential difference between A and B?

1. Assume the electric field E in some region is uniform: it is the same at all points. Specifically, E has a magnitude of 5 V/m and points in the +x direction. What can you then say about the behavior of the electric potential a) in the x-direction and b) in the y-direction? Explain your answers. 2. Suppose you have a uniform Electric field with a magnitude of 5 V/m in the +x direction. (i) What can you say about the potential difference between two points separated by a distance of 2 m along the x-axis? (ii) What can you say about the potential difference between two points separated by a distance of 3 m along the y-axis? (iii) Is your answer to this question consistent with the answer to question 1?

The diagram represents a contour map of hilly island. Copy it into your lab notebook. The outer contour of the figure is at sea level. All points on any one particular contour line are at same elevation (vertical distance above sea-level). The distance between any two contour lines in the diagram represents the horizontal distance between points on the two different countours.  North is up. The same diagram could also represent the contours of the electrical potential of two positively charged objects with irregular shapes (for example charges stored on a rubber sheet). Assume that the outer part of the figure is at zero potential. Each contour line going towards the center represents an equipotential surface with a potential 5 V greater than the previous contour. a) Where is the electric field particularly strong? Show at least three places. Explain your reasoning with reference to Q1(a).b) There are two areas of high potential on the diagram. What is the value (in Volts) of c)  each of these high potential peaks? c) What path would require you to use the least amount of force to push a test charge from zero potential to the point of highest potential of one of the charged objects? (Choose the same one you labeled B in 1b) above.) Explain your reasoning. d) Would you actually do less work to move the test charge from 0 V to the voltage at B by using the path selected in 2c), or would the actual path make no difference? 

An electron is projected with an initial speed v0 = 1.10 × 106 m/s into the uniform field between the parallel plates in the figure. Assume that the field between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. The electron enters the field at a point midway between the plates.The electron just misses the upper plate as it emerges from the field.(a) Suppose that in the figure, the electron is replaced by a proton with the same initial speed. Would the proton hit one of the plates?(b) What would be the direction of proton's displacement? Upward or downward?

What unit is represented by(a) joule per coulomb,(b) coulomb per second, and(c) watt-second?

1. In the figure, which capacitor plate, left orright, is the positive plate?2. What is the electric field strength insidethe capacitor?3. What is the potential energy of a proton atthe midpoint of the capacitor?

An electron with an initial speed of 500,000 m/s is brought to rest by an electric field.a. Did the electron move into a region of higher potential or lower potential?b. What was the potential difference that stopped the electron?c. What was the initial kinetic energy of the electron, in electron volts?

An electron moves along the trajectory from i to f in Figure Q21.5.a. Does the electric potential energy increase, decrease, or stay the same? Explain.b. Is the electron's speed at f greater than, less than, or equal to its speed at i? Explain.

A proton with an initial speed of 900000 m/s is brought to rest by an electric field.Part A- Did the proton move into a region of higher potential or lower potential?Part B - What was the potential difference that stopped the proton?ΔU = ________VPart C - What was the initial kinetic energy of the proton, in electron volts?Ki =_________eV

Two positive charges are equal. Which has more electric potential energy?a. Both have zero potential energyb. Charge Ac. Charge Bd. They have the same potential energy

Consider a uniformly charged ring in the xy plane, centered at the origin. The ring has radius a and positive charge q distributed evenly along its circumference. Part A. What is the direction of the electric fieldat any point on the z axis?A. parallel to the x axisB. parallel to the y axisC. parallel to the z axisD. in a circle parallel to the xy plane

As a proton moves in the direction the electric field lines:a. it is moving from low potential to high potential and gaining electric potential energy.b. it is moving from low potential to high potential and losing electric potential energy.c. it is moving from high potential to low potential and gaining electric potential energy.d. it is moving from high potential to low potential and losing electric potential energy.e. both its electric potential and electric potential energy remain constant.

Part A Determine the magnitude and direction of the electric field at point 1 in the figureE1→=(2500V/m,up) E1→=(7500V/m,up) E1→=(3750V/m,down) E1→=(2500V/m,down) 

Determine the magnitude and direction of the electric field at point 2 in the figure. A. E2=(2500V/m,up) B. E2=(3750V/m,down) C. E2=(7500V/m,down) D. E2=(5000V/m,up) 

Suppose you have a uniform Electric field with magnitude of 5 V/m in the +x direction. (a) What can you say about potential difference between two points separated by a distance of 2 m along the x-axis? (b) What can you say about potential difference between two points separated by a distance of 3 m along the y-axis?

Consider a uniformly charged ring in the xy plane, centered at the origin. The ring has radius a and positive charge q distributed evenly along its circumference. What is the magnitude of the electric field along the positive z axis?Use k in your answer where:k=14πε0E(x) = ______

A 9.0×10−2 g plastic bead is charged by the addition of 1.0×1010 excess electrons.Part AWhat electric field E⃗  (strength) will cause the bead to hang suspended in the air?Part BWhat electric field E⃗  (direction) will cause the bead to hang suspended in the air?

Suppose you have an electric field that exerts a 2.05 × 10–5 N upward force on a –1.6 μC charge. Calculate the vertical component of the electric field, in Newtons per coulomb, taking up to be the positive direction.

The electric field strength is 5.00×104N/C inside a parallel-plate capacitor with a 1.90mm spacing. A proton is released from rest at the positive plate. What is the proton's speed when it reaches the negative plate?

Large electric fields in cell membranes cause ions to move through the cell wall. The field strength in a typical membrane is 1.0 x 107 N/C.(a) What is the magnitude of the force on a calcium ion with charge +e? (b)What is its acceleration?(c) Is it possible for a particle with the same charge as as calcium to have a different acceleration if placed at this location?(d) What would change the acceleration: mass of the particle? diameter of the particle?

A negative charge (q=-0.55 coulombs) is placed above the floor that has a positive charge. The floor creates a uniform electric field that has a magnitude of 105 N/C.a) What is the magnitude and direction of the electric force caused by the floor on the negative charge?b) If the charge is initially at a distance 2.5m above the plane, what will the change in electric potential energy (in joules) be if it is then moved to a distance 1.25m above the plane? (specify whether this change is positive/negative/zero).

In one of the classic nuclear physics experiments at the beginning of the 20th century, an alpha particle was accelerated toward a gold nucleus, and its path was substantially deflected by the Coulomb interaction. If the energy of the doubly charged aplha nucleus was 5.00 MeV, how close to the gold nucleus (79 protons) could it come before being deflected?

A +3.0nC charge is at x=0cm and a 1.0nC charge is at x=4.0cm. At what point or points on the x-axis is the electric potential zero?

Suppose a point charge produces a potential of -1.7 V at a distance of 1.8 mm.What is the charge, in coulombs, of the point charge?

A particle of charge q > 0 moves in a uniform electric field E under no external force for a total distance d starting from restPart (a) Suppose the field is varying according to E = (2/11) Ayj, where y is the vertical coordinate. The charge q travels from point y1 to point y2, where the total traveled distance is d. Taking y1 = 0, enter an expression for the potential difference that the charge traverses in terms of the available symbolsPart (c) If the charge q = 4.72 C, distance, d = 82m and the constant A = 14.7 V/m2,  how much work, in Jules, is done on the charge while it travels the potential difference in part (a)?

As an electron moves in the direction of the electric field lines...Answer: It is moving from high potential to low potential and gaining electric potential energy.Explain why the electron is gaining electric potential energy if it is moving from high to low potential energy?

Consider an experimental setup where charged particles (electrons or protons) are first accelerated by an electric field and then injected into a region of constant magnetic field with a field strength of 0.25 T. What is potential difference, in volts, required in the first part of the experiment to accelerate electrons to a speed of 6.1x107 m/s?

An electron with an initial speed of 5.50×105 is brought to rest by an electric field. (a) Did the electron move into a region of higher potential or lower potential? (b) What was the potential difference that stopped the electron? In V (c) What was the initial kinetic energy of the electron, in electron volts? In eV

A proton with an initial speed of 650,000 m/s is brought to rest by an electric field.1. What was the potential difference that stopped the proton?2. What was the initial kinetic energy of the proton, in electron volts?

A proton with an initial speed of 600,000 m/s is brought to rest by an electric field.What was the potential difference that stopped the proton?

If a proton is accelerated from rest through a potential difference of 1500 V, find its final velocity. proton mass = 1.67 × 10−27 kg. Hint- first find its kinetic energy, then its velocity.

A proton with an initial speed of 600,000 m/s is brought to rest by an electric field.What was the initial kinetic energy of the proton, in electron volts?

Find the ratio of speeds of an electron and a negative hydrogen ion (one having an extra electron) accelerated through the same voltage, assuming non-relativistic final speeds. Take the mass of the hydrogen ion to be 1.67x10-27 kg.

An electron with an initial speed of 5.30×105 m/s is brought to rest by an electric field.What was the potential difference that stopped the electron?

What is the speed of a proton that has been accelerated from rest through a potential difference of -1000V?Express your answer to two significant figures and include the appropriate units.

Consider an oil droplet of mass m and charge q.  We want to determine the charge on the droplet in a Millikan-type experiment. We will do this in several steps. Assume, for simplicity, that the charge is positive and that the electric field between the plates points upward.a. An electric field is established by applying a potential difference to the plates. It is found that a field of strength E0 will cause the droplet to be suspended motionless. Write an expression for the droplet's charge in terms of the suspending field E0 and the droplet's weight mg.b. The field E0 is easily determined by knowing the plate spacing and measuring the potential difference applied to them. The larger problem is to determine the mass of a microscopic droplet. Consider a mass  falling through viscous medium in which there is a retarding or drag force. For very small particles, the retarding force is given by Fdag g = -bv  where b is a constant and v the droplet's velocity. The sign recognizes that the drag force vector points upward when the droplet is falling (negative v). A falling droplet quickly reaches a constant speed, called the terminal speed vterm. Write an expression for the terminal speed vterm in terms of m, g, and b.

Consider two points in an electric field. The potential at point 1, V1, is 31 V. The potential at point 2, V2, is 168 V. An electron at rest at point 1 is accelerated by the electric field to point 2.Part (a) Write an equation for the change of electric potential energy ΔU of the electron in terms of the symbols give.Expression:ΔU = ________Select from the variables below to write your expression. Note that all variables may not be required. α, β, ΔU, θ, d, e, g, h, I, m, me, P, t, V1, V­2Part (b) Find the numerical value of the change of the electrical potential energy in electron volts (eV).Numeric: A numeric value is expected and not an expressionΔU = __________

Part A. The electric potential along the x-axis is V =200x2 V, where x is in meters. What is Ex at x =0 m? Express your answer as an integer and include the appropriate units.Part B. What is Ex at x =3 m? Express your answer to three significant figures and include the appropriate units.

If the electric potential at some point is large, is the electric field at that point also necessarily large or not? Explain your answer, and provide a counterexample if not. 1. 

An electron with an initial speed of 5.00×105 m/s is brought to rest by an electric field.A. Did the electron move into a region of higher potential or lower potential?B. What was the potential difference that stopped the electron?C. What was the initial kinetic energy of the electron, in electron volts?

A free positive charge released in an electric field will a. accelerate in a direction perpendicular to the electric field. b. remain at rest. c. accelerate in the direction opposite the electric field. d. accelerate in the same direction as the electric field is pointing. e. accelerate along a circular path.

The electric potential in a certain region is plotted in the following graph1. At which point is the magnitude of the E-field greatest?2. At which point is the direction of the E-field along the negative x-axis?

Two charged rods, each with net charge -Qo, are held in place as shown in the top view diagram below. A small test charge -qo travels from point X to point Y along the circular are shown. Draw an arrow on the diagram at each point (X and Y) to show the direction of the electric force on the test charge at that point. Explain why you drew the arrows as you did.

For a positive charge moving in the direction of the electric field,a) its potential energy increases and its electric potential decreases.b) its potential energy decreases and its electric potential decreases.c) its potential energy decreases and its electric potential increases.d) its potential energy and its electric potential both remain constant.e) its potential energy increases and its electric potential increases.

An electron is projected with an initial speed v0 = 1.10 × 106 m/s into the uniform field between the parallel plates in the figure. Assume that the field between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. The electron enters the field at a point midway between the plates.The electron just misses the upper plate as it emerges from the field. Suppose that in the figure, the electron is replaced by a proton with the same initial speed.Compare the paths traveled by the electron and the proton and explain the differences.

A proton is released from rest at the dot. Afterward, the protona) Remains at the dot.b) Moves upward with steady speed.c) Moves downward with a steady speed.d) Moves downward with an increasing speed.e) Moves upward with an increasing speed.

A point charge with charge q1 is held stationary at the origin. A second point charge with charge q2 moves from the point (x1, 0) to the point (x2, y2).How much work W is done by the electrostatic force on the moving point charge?Express your answer in joules. Use k for Coulomb's constant (k=1/(4πε0)).