Two charges of equal magnitude, but opposite sign, are situated on the x-axis as shown. What is the direction of the electric field at the origin? y r q -q X a) Zero (there is no field at the origin) b) Up c) Down r

Consider n equal positively charged particles each of magnitude Q/n placed symmetrically around a circle of radius a. (a) Calculate the magnitude of the electric field at a point a distance x from the center of the circle and on the line passing through the center and perpendicular to the plane of the circle. (b) Explain why this result is identical to the result of the calculation done in Example 23.8.

A sphere has a net charge of 8.05 nC, and a negatively charged rod has a charge of 6.03 nC. The sphere and rod undergo a process such that 5.00 109 electrons are transferred from the rod to the sphere. What are the charges of the sphere and the rod after this process?

A rod 14.0 cm long is uniformly charged and has a total charge of 22.0 C. Determine (a) the magnitude and (b) the direction of the electric field along the axis of the rod at a point 36.0 cm from its center.

Point charges of 25.0 C and 45.0 (2 are placed 0.500 m apart. (a) At what point along the line between them is the electric field zero? (b) What is the electric field halfway between them?

A test charge of +3 C is at a point P where an external electric field is directed to the right and has a magnitude of 4 06 N/C. If the test charge is replaced with another charge of 3 C, what happens to the external electric field at P? (a) It is unaffected. (b) It reverses direction. (c) It changes in a way that cannot be determined.

Three equal positive charges q are at the comers of an equilateral triangle of side a as shown in Figure P19.28. Assume the three charges together create an electric field. (a) Sketch the field lines in the plane of the charges. (b) Find the location of one point (other than ) where the electric field is zero. What are (c) the magnitude and (d) the direction of the electric field at P due to the two charges at the base?

Two point particles with charges +3C and +5C are held in place by 3-N forces on each charge in appropriate directions. (a) Draw a free-body diagram for each particle. (b) Find the distance between the charges.

Two point charges attract each other with an electric force of magnitude F. If the charge on one of the particles is reduced to one-third its original value and the distance between the particles is doubled, what is the resulting magnitude of the electric force between them? (a) 112F (b) 13F (c) 16F (d) 34F (e) 32F

Assume the charged objects in Figure OQ23.10 are fixed. Notice that there is no sight line from the location of q2 to the location of q1. If you were at q1, you would be unable to see q2 because it is behind q3. How would you calculate the electric force exerted on the object with charge q1? (a) Find only the force exerted by q2 on charge q1. (b) Find only the force exerted by q3 an charge q1. (c) Add the force that q2 would exert by itself on charge q1 to the force that q3 would exert by itself on charge q1. (d) Add the force that q3 would exert by itself to a certain fraction of the force that q2 would exert by itself. (e) There is no definite way to find the force on charge q1.