Solve the following problems on your own paper. Please:

• Show all work.
• Put a box around your final answer to each problem.
• Be sure proper significant figures (SF) used for all answers.
• Separate all solutions with a horizontal line on your paper.
• A random selection of five problems will be graded for 20 points each.
• Solutions for suggested odd problems can be seen by following links.
• Solutions for assigned problems will be linked from this page after the due date.

Chapter 21

#4

If it is easier for you, assume both charges are just 1.00 C, then solve the problem numerically. Answer with 2 SF.

#16

See the example on the right hand side of page 568 for some guidance. For (a), the y-components cancel. For (b), the x-components cancel.

#24

For part (b), the total number of electrons is just the total charge divided by the charge per electron, e.

#34

For circular orbits like this, similar to satellite orbits around planets, you can use the logic found on page 345 in the chapter on gravity and orbits. In this case, gravity is not the attracting force. Instead, it is the Coulomb force.

#40

Write an expression for the total force, F, then take dF/dx and set equal to zero to find the minimum. For the algebra, you can greatly simply things if you take the cube root of both sides instead of expanding out (L-x)^3, etc.

#46

This is simple if you are careful with the signs on your forces.

#60

Balance electric and gravitational forces here. Answer with 2 SF.

Suggested problems from chapter 21:

1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 21, 22, 23, 25, 26, 33, 35, 37, 39, 41, 53, 61

Chapter 22

#6

The answer is *not* zero. Be sure to get signs right in this problem.

#8

Note that in between the two particles, the electric field cannot be zero since the field due to each particle will point in the -x direction. So first decide where the field will be zero (to the right or left of the particles?). There is a math trick here near the end similar to that from Ch 21, problem 40 (take the square root of both sides instead of expanding the binomial). You do not need to do part (b).

#12

First calculate the distance from each charge to point P. It is the same in each case. Recall that a micrometer is 10^(-6) meters.

#24

See sample problem 22-4 for some help here. Problems 25 and 28 are similar.

#26

This problem simply involves taking the derivative of the expression for the electric field with respect to z, then set it equal to zero.

#32

This is easier if you just solve for the z=4.0 case (see graph).

#40

You can use F = ma and equations from chapter 2 (page 23) to solve this, or you can use work-energy concepts.

#46

This is similar to problem 44 and also most ballistic motion problems (in which the acceleration affects only one component in the problem while motion in the other component is constant).

Suggested problems for chapter 22:

4, 5, 9, 10, 11, 13, 14, 15, 17, 18, 19, 22, 23, 25, 27, 28, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 47, 48, 49, 55, 58