1. In the following problems, you don't need to understand the physics to complete the questions. Focus on the equations. (a) The force of gravity, F, between two masses, m and M, separated by a distance r, is given where G is a constant. Write an equation of r in terms of other variables in the GmM by F= 2 equation for F: r= (b) The electric force between two charges q=3.106 units and Q=-4.106 units separated by a distance, kqQ d² d = 3. 10-4 units, is given by F= - where k=9. 10⁹ units. Without using a calculator, calculate the F. F=
1. In the following problems, you don't need to understand the physics to complete the questions. Focus on the equations. (a) The force of gravity, F, between two masses, m and M, separated by a distance r, is given where G is a constant. Write an equation of r in terms of other variables in the GmM by F= 2 equation for F: r= (b) The electric force between two charges q=3.106 units and Q=-4.106 units separated by a distance, kqQ d² d = 3. 10-4 units, is given by F= - where k=9. 10⁹ units. Without using a calculator, calculate the F. F=
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. In the following problems, you don't need to understand the physics to complete the
questions. Focus on the equations.
(a) The force of gravity, F, between two masses, m and M, separated by a distance r, is given
where G is a constant. Write an equation of r in terms of other variables in the
GmM
by F=
I
2
equation for F:
r=
(b) The electric force between two charges q=3∙10-6 units and Q= −4.
by a distance,
-4.10-6
d = 3. 10-4 units, is given by F=
kqQ
d²
where k=9. 10⁹ units.
Without using a calculator, calculate the F.
F=
units separated
Transcribed Image Text:(c) Two positive electric charges, q and Q are separated by a distance d. Assume that q> Q>0.
The position x from charge q where the electric field zero is given by:
kq
kQ
x² (d-x)²
=
Solve for x in terms of the other variables. The quantity k is a constant. Solution 1 represents
the largest value of x.
Hint: The solution can be simplified in many ways. The solutions accepted below have a form
Solution 1 =
Solution 2 =
d
b√2/20
a-b
d
Q
+b√2
a+b
You need to figure out the constants a and b in each case.
Solution 1: x=
Solution 2: x=
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