Wiley Conceptual Questions: Honors Physics, Electrostatics

Consider the following four possibilities for two point charges and choose the one(s) that do not change the magnitude of the electrostatic force that each charge exerts on the other: A. Double the magnitude of each charge and double the separation between them.B. Double the magnitude of each charge and reduce the separation between them to half of its initial value.C. Double the magnitude of only one charge and double the separation between the charges.D. Double the magnitude of only one charge and increase the separation between the charges by a factor of root 2.

A and D Explanation: Coulomb's law states that the magnitude of the force is given by F=K*q1*q2/r^2. Doubling the magnitude of each charge as in A would increase the numerator by a factor of four, but this is offset by the change in separation, which increases the denominator by a factor of 2^2 = 4. Doubling the magnitude of only one charge as in D would increase the numerator by a factor of two, but this is offset by the change in separation, which increases the denominator by a factor of root 2=2

Three point charges have equal magnitudes and are fixed to the corners of an equilateral triangle. Two of the charges are positive and one is negative, as the drawing shows. At which one of the corners is the net force acting on the charge directed parallel to the x axis?

B

Three point charges have equal magnitudes and are located on the same line. The separation d between A and B is the same as that between B and C. One of the charges is positive and two are negative, as the drawing shows. Consider the net electrostatic force that each charge experiences due to the other two charges. Rank the net forces in descending order (greatest first) according to magnitude.

B,A,C

The drawing shows some electric field lines. For the points indicated, rank the magnitudes of the electric field in descending order (largest first).

B,C,A

The drawing shows an electric field line. What are the directions of the electric fields at points A, B, and C?

Due south at A, southeast at B, due east at C

Because of an electric field, a positive charge +q experiences a force of magnitude F that points due west. The positive charge is then replaced with a negative charge -2q. What force does the negative charge experience?

Force magnitude = 2F, force direction is due east

Each of two identical objects carries a net charge. The objects are made from conducting material. One of them is attracted to a positively charged ebonite rod, and the other is repelled by the rod. After the objects are touched together, it is found that they are each repelled by the rod. What can be concluded about the initial charges on the objects?

Initially one object is positive and one is negative, with the positive charge having a greater magnitude than the negative charge. Explanation: The fact that the positive rod repels one object indicates that that object carries a net positive charge. The fact that the rod repels the other object indicates that that object carries a net negative charge. Since both objects are identical and made from conducting material, they share the combined net charges equally after they are touched together. Since the rod repels each object after they are touched, each object must then carry a net positive charge. But the net electric charge of any isolated system is conserved, so the total net charge initially must also have been positive. This means that the initial positive charge had the greater magnitude.

Three point charges (some positive and some negative) are fixed to the corners of the same square in various ways, as the drawings show. Each charge, no matter what its algebraic sign, has the same magnitude. In which arrangement (if any) does the net electric field at the center of the square have the greatest magnitude?

The magnitude of the net field at the center of the square is the same in each arrangement of the charges.

A positively charged ebonite rod is brought close to a small ball. The rod does not touch the ball, which is made from a conducting material. The ball is electrically neutral. Which one of the following statements is true?

The rod attracts the ball Explanation: The ball is electrically neutral (net charge equals zero). However, it is made from a conducting material, so it contains electrons that are free to move. The rod attracts some of these (negative) electrons to the side of the ball nearest the rod, leaving the opposite side of the ball positively charged. Since the negative side of the ball is closer to the positive rod than the positive side, a net attractive force arises.

The drawing shows a positive and a negative point charge. The negative charge has the greater magnitude. Where on the line that passes through the charges is the one spot where the total electric field is zero?

To the left of the positive charge.

You have two identical metal spheres and a negatively charged ebonite rod. Without touching the rod to the spheres, which one of the following procedures can you use to give each sphere a net electrical charge of the same magnitude, one being positive and the other being negative.

Touch the two spheres together. Bring the rod near one sphere, opposite the place where the spheres are touching. Then, with the rod in place, separate the spheres. Explanation: This is an example of charging by induction. The negatively charged rod repels free electrons in the metal. These electrons move through the point of contact and into the sphere farthest away from the rod, giving it an induced charge of -q. The sphere nearest the rod acquires an induced charge of +q. As long as the rod is kept in place while the spheres are separated, these induced charges cannot recombine and remain on the spheres.

A positive point charge q1 creates an electric field of magnitude E1 at a spot located at a distance r1 from the charge. The charge is replaced by another positive point charge q2, which creates a field of magnitude E2 = E1 at a distance of r2 = 2r1. How is q2 related to q1?

q2 = 4q1