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? 

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

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?

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?

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?

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 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?

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?

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. 

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?

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.