Problem 3: A model of a singly ionized helium atom consists of a single electron moving in a circular orbit of radius 0.025 nm around a nucleus consisting of two protons and two neutrons. For this model:

a) What is the magnitude of the electric field of the proton at the electron?

b) How many revolutions per second does the electron make?

Problem 4: Objects A and B are both positively charged. Both have a mass of 100 g, but A has twice the charge of B. When A and B are placed 10 cm apart, B experiences an electric force of 0.45 N. a) What is the charge on A b) If the objects are released, what is the initial acceleration of A? c) What is the magnitude of the electric field originating from charge B evaluated at charge A?

Problem 5: A 0.10 g honeybee acquires a charge of +23 pC while flying. Note: 1 pC = 10-12C.

a) The earth’s electric field near the surface is typically (100 N/C, downward). What is the ratio of the electric force on the bee to the bee’s weight?

b) What electric field (magnitude and direction) would allow the bee to hang suspended in the air?


Problem 6: You sometimes create a spark when you touch a doorknob after shuffling your feet on a carpet. Why? The air always has a few free electrons that have been kicked out of atoms by cosmic rays. If an electric field is present, a free electron is accelerated until it collides with an air molecule. It will transfer its kinetic energy to the molecule, then accelerate, then collide, then accelerate, collide, and so on.

If the electron’s kinetic energy just before a collision is 2.0 × 10−18???? or more, it has sufficient energy to kick an electron out of the molecule it hits. Where there was one free electron, now there are two! Each of these can accelerate, hit a molecule, and kick out another electron. Then there will be four electrons. In other words, a sufficiently strong electric field causes a “chain reaction” of electron production. This is called a breakdown of the air. The current of moving electrons is what gives you the shock, and a spark is generated when the electrons recombine with the positive ions and give off excess energy as a bust of light.

a) The average distance an electron travels between collisions is 2.0 m. What acceleration must an electron have to gain 2.0 × 10−18???? of kinetic energy in this distance?

b) What force must act on an electron to give it the acceleration found in part a?

c) What strength electric field will exert this much force on an electron? This is the breakdown field strength.

d) Suppose a free electron in air is 1.0 cm away from a point charge. What minimum charge must this point charge have to cause a breakdown of the air in create a spark?