Download Homework 1 Solution

Homework 1
Practice Problems from Chapter 19
Point Charges
5, 7, 8, 11, 12
Coulomb’s Law between Point Charges
13, 14, 15, 17, 21, 23, 27, 29, 30, 31, 34, 41
Electric Field from Point Charges
42, 43, 44, 45, 47, 49, 50, 51, 52
A note about the solution to the graded problem.
A solution should contain a short explanation about what you are doing at every physics step.
You don’t have to explain the math steps. Also, show the physics equations you are using before
you use them. Lay out the value for each variable before the substitution is good practice. Finally,
make sure you answer the question and not stop just because the math is done.
The following example contains the minimum required explanation.
Example Question
How much time does it take a 1 kg mass, when released from rest, to fall a distance of 1 meter?
Example Solution
1. This part states the model or equation you are using and the reason that allows you to use it.
Since the mass is at the surface of the Earth, its acceleration is a constant 9.8 m/s2. We can use
the following constant-acceleration equations of motion,
1
Δy = vi,y Δt + ay Δt 2
2
2. This part describes the variables for the equation. You should define your coordinate system as well.
The vertical displacement is –1 meter. The initial velocity is 0 m/s. The acceleration is –9.8 m/s2.
3. This part is just math. Don’t rush.
1
−1 = (−9.8)Δt 2
2
⇒ Δt = 0.45 s
4. This part is the answer. The actual answer to the question is not necessarily the same as the math result.
The time required for an object released from rest to fall a distance of 1 meter is 0.45 seconds.
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Graded Problem Due Tuesday, 9/29/15
A carbon atom has 6 protons in its nucleus. Approximate the nucleus as a point charge. One
electron is orbiting this nucleus; that is, the electron is moving around the nucleus in a circle at a
constant speed.
a. What is the magnitude of the electric field due to the nucleus 1 angstrom (10-10 m) from the
nucleus? In which direction does it point?
b. What is the magnitude of the electric force due to the nucleus on the electron 1 angstrom from
the nucleus? In which direction does it point?
c. How much kinetic energy does the electron have?
Solution
a. The magnitude of the electric field due 6 protons at 1 angstrom is this.
2⎞
−19
⎛
qsource
C)
N
9 Nm ⎟ 6(1.6 ×10
⎜
⎟
E = k 2 = ⎜ 8.99 ×10
= 8.63 ×1011
2 ⎟
−10
2
⎜
⎟
C
r
C ⎠ (10 m)
⎝
Because the source charges is positive, the direction of the electric field is radially outward.
b. The magnitude of the electric force between 6 protons and 1 electron 1 angstrom apart is this.
⎛
N ⎞⎟
F = qtest E = 1.6 ×10−19 C ⎜⎜ 8.63 ×1011
⎟ = 1.38 ×10−7 N
⎜⎝
C ⎟⎟⎠
Because the two charges are opposite, the direction of the force on the electron is radially inward.
c. The electron is moving in a circle. The net force in the radial direction is the centripetal force.
ΣFradial
mv 2
=
r
The only force (radial or otherwise) is the electric force.
Fe = 1.38 ×10−7 N =
mv 2 / 2 2
= K = 2 ×1010 K
r/ 2
r
⇒ K = 6.90 ×10−18 J
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