a) The two charges have opposite signs, so they attract. Q2 is located on the positive x axis, to the right of Q1 at the origin. The force on Q1 due to Q2 will be toward Q2, in the positive x direction.

d) The two charges still have opposite signs, so they still attract. Now Q2 is located at the origin, to the left of Q1. The force on Q1 due to Q2 will be toward Q2, in the negative x direction.

Newton’s third law tells us that the force of attraction has the same magnitude for each of the lightning bugs.

d) The strength of the field is proportional to the spacing/density of the field lines. At point 1 the field lines are spaced more closely than they are at point 2. Therefore, the electric field at point 1 is stronger than the electric field at point 2.

d) Remember which object is creating the electric field we’re interested in, and which object is the “test charge” interacting with this field. Here, the positive point charge is creating the field, and the field created by a positive charge always points directly away from it. When a negative charge sits in an electric field, it feels a force in the opposite direction as the field. That is, the negative charge experiences a force toward the positive charge. This all makes sense, because opposite charges attract.

a) An object acquires a positive charge when it loses electrons, which mean the object’s mass decreases.

a)The plates are not like point charges, with the electric field decreasing with distance. The electric field lines created by a charged plate are parallel with equal spacing. Bringing the plates closer has little effect on the electric field between them.

b) The positive test charge repels charges on the surface of the conductor, which then slide along the surface to get farther away from the test charge. By being farther from the point being considered, they contribute a smaller amount to the field there. That is why a very small test charge is specified.

d) One can check that the electric force between charged subatomic particles is about 1036 times greater than the gravitational attraction between them. We don’t notice electric forces between everyday objects because most of them are very close to being electrically neutral. We do notice the electric force when everyday things have a net charge (such as a balloon rubbed against one’s hair).

b) Hiding inside a metal car is like being in a cavity within a conductor, which shields you from external electric fields.

a)c)e) Lightning generally strikes the tallest conductors in the region. The poor choices in A, C, E make a person more likely to be struck by lightning.

d) The electric field at the lower-right-hand corner is the vector sum of the electric fields caused by the charges at the other three corners. The two positive charges in the lower left and upper right create equal-magnitude E fields pointing in the positive x direction and in the negative y direction, respectively. These add to produce an electric field in the direction of choice D. By the Pythagorean theorem, this field has a strength of 2√ times the magnitude of the E field due to just one of the charges. The E field created by the remaining negative charge points in the direction of choice B. Because the negative charge is 2√ times farther away than either of the positive charges, the magnitude of its electric field is insufficient to cancel the field from the 2 positive charges. The net field points in the direction of (d).

e) If the metal ball is negatively charged it will be attracted. However, even a neutral conductor will become polarized as negative charges move to the side of the ball closer to the positively charged rod. Then the ball will be attracted to the positively-charged rod; The attraction between the unlike charges dominates the repulsion between the like charges because the unlike charges are closer.