Electric field

a) Students should understand the concept of the electric field, so they can:

1) Define it in terms of the force on a test charge.

2) Describe and calculate the electric field of a single point charge.

3) Calculate the magnitude and direction of the electric field produced by two or more point charges.

4) Calculate the magnitude and direction of the force on a positive or negative charge placed in a specified field.

5) Interpret an electric field diagram.

6) Analyze the motion of a particle of specified charge and mass in a uniform electric field.

b) Students should understand the concept of electric potential, so they can:

APC-EField     Source: A-Plus Physics

1.3 – Electric Fields

Electric Fields The electric field can be thought of as a map which depicts the amount and direction of the force that a positive charge would experience if placed at each point in the map, divided by that charge. The fact that the electric field is a force per unit charge means that the electric field strength is independent of the charge placed in the field.   Electric Fields around Point Charges   Consider an extremely small charge q a distance r away from a comparatively large charge Q.  The force on charge q can be found using Coulomb’s Law. If the charge were replaced with a 2q charge, the force on it would be twice as large.    Charge Q exerts a force on charge q over a distance. It is helpful to think of charge Q creating a “field” around it that effects other charges placed in that area. The magnitude of this electric field can be found at any point. The direction of the field at any point in space is determined by the direction of the force exerted on a positive test charge placed at that point.  A test charge is an hypothetical, infinitesimally small charge used only to visualize the electric field.   Visualizing Electric Fields Using the idea of a test charge, we can imagine the electric field around several charge configurations.  Electric field lines start from either a positive charge, or infinity, and end at either a negative charge or infinity. Electric field lines never cross. The magnitude of the electric field is proportional to the density of the electric field lines.       Parallel Plates     The electric field between parallel plates is uniform.  Near the edge of the plates, the electric field is not uniform and weaker. This is called “edge effects”, and when spacing between the plates is small compared to the size of the plates, we can often neglect these effects.   Example 1 – Parallel Plates The following questions refer to the figure shown. a. An electron is placed at point B between two parallel plates shown on the right. The electric field created by the parallel plates is directed upward.  downward. b. An electron is placed at point B between two parallel plates shown on the right. The electric force on the electron is directed toward point A. toward point C.  to the right.  to the left . There is no force. c. An electron is placed near the negative plate and moves towards the positive plate, passing through points A, B, and C. The electron will experience the greatest force when at point A  point B  point C  The force is the same at all three points. d. An electron is placed near the negative plate and moves towards the positive plate, passing through points A, B, and C. The electron will experience the greatest acceleration when at point A  point B  point C  The acceleration is the same at all three points. e. An electron is placed near the negative plate and moves towards the positive plate, passing through points A, B, and C. The electron will experience the greatest speed when at point A  point B  point C  The speed is the same at all three points. f. An electron is placed near the negative plate and moves towards the positive plate, passing through points A, B, and C. The electron has the greatest kinetic energy at the negative plate.  at point B.  the positive plate.  The electron has the same KE at all points. g. An electron is placed near the negative plate and moves towards the positive plate, passing through points A, B, and C. The electron has the greatest electric potential energy at the negative plate.  the positive plate.  at point B.  The electron has the same UE at all points. h. An electron is placed at point B. It would take positive work to move the electron to point A.  point C.  It does not take any work to move the electron between parallel plates. i. Compared to an electron, if proton were placed at point B, it would experience greater force.  the same force.  a smaller force. j. Compared to an electron, if proton were placed at point B, it would experience a greater acceleration.  the same acceleration.  a smaller acceleration.   Electric Fields Inside of Conductors The electric field everywhere inside a conductor when charges are not moving must be zero. If it were not, the charges would have a force exerted on them, and they would move.  This results in all of the net charge on a conductor residing on its surface.  Electric field lines are always perpendicular to the surface of a conductor.  These properties only apply to conductors.  Inside of insulators, where electrons are not free to move about, there can be electric fields.   Example 2 – Electric Field along a line containing Two Point Charges a. Find the electric field due to charges 1 and 2 at point A. b. Find the electric field due to charges 1 and 2 at point B. c. At point C, the electric field is zero. Calculate x.     Example 3 – Electric Field on a Two Dimensional Plane Find the electric field at points A and B.

1.4 – Electric Fields and Continuous Charge Distributions

Continuous Charge Distributions For many symmetrically charged objects we can find the electric field by breaking the charge up into infinitesimal charges dq, each of which will act as a point charge. Each dq contributes dE to the electric field. The electric field at that point can be found summing over all the dE’s. Example 1 – A Ring of Charge A ring of radius a lies in the the yz-plane and is centered around the x-axis. It has a total charge +Q uniformly distributed around it. Find the electric field at all points along the x-axis. Example 2 – A Long Line of Charge Find the electric field at all points around a wire of uniform charge per unit length λ. Example 3 – A Uniformly Charged Disk A disk of radius R has a uniform charge per unit area of σ. a. Calculate the electric field a distance x away from the center of the disk. b. What is the electric field close to the uniformly charged disk (x<<R)? This is the electric field anywhere above or below a uniformly charged infinite plane.Example 4 – Parallel Plates Using your answer from Example 3, determine the electric field between parallel plates, one of which is carrying a uniform charge density +σ and the other a uniform charge density –σ. What assumptions must we make for this to hold true?

1.5 – Gauss’ Law

Electric Flux Electric flux is proportional to the number of electric field lines that cross an area. Where   is the electric flux (N·m2/C)               is the electric field (N/C) is the area (m2) is the angle between the E and A Note that the direction of the area is perpendicular to the plane formed by the area.

Electric Potential

1) Determine the electric potential in the vicinity of one or more point charges.

2) Calculate the electrical work done on a charge or use conservation of energy to determine the speed of a charge that moves through a specified potential difference.

3) Determine the direction and approximate magnitude of the electric field at various positions given a sketch of equipotentials.

4) Calculate the potential difference between two points in a uniform electric field, and state which point is at the higher potential.

5) Calculate how much work is required to move a test charge from one location to another in the field of fixed point charges.

6) Calculate the electrostatic potential energy of a system of two or more point charges, and calculate how much work is required to establish the charging system.

7) Use integration to determine the electric potential difference between two points on a line, given electric field strength as a function of position along that line.

8) State the general relationship between field and potential, and define and apply the concept of a conservative electric field.

APC-EPotential    Source: A-Plus Physics