Respuesta :
Answer:
charge on each
Q1 = 2.06 ×[tex]10^{-5}[/tex] C
Q2 = 7.23 × [tex]10^{-5}[/tex] C
when force were attractive
Q1 = 1.07 × [tex]10^{-4}[/tex] C
Q2 = -1.39 × [tex]10^{-5}[/tex] C
Explanation:
given data
total charge = 93.0 μC
apart distance r = 1.14 m
force exerted F = 10.3 N
to find out
What is the charge on each and What if the force were attractive
solution
we know that force is repulsive mean both sphere have same charge
so total charge on two non conducting sphere is
Q1 + Q2 = 93.0 μC = 93 ×[tex]10^{-6}[/tex] C
and
According to Coulomb's law force between two sphere is
Force F = [tex]\frac{K Q1 Q2 }{r^2}[/tex] .........1
Q1Q2 = [tex]\frac{F*r^2}{k}[/tex]
here F is force and r is apart distance and k is 9 × [tex]10^{9}[/tex] N-m²/C² put all value we get
Q1Q2 = [tex]\frac{ 10.3*1.14^2}{9*10^9}[/tex]
Q1Q2 = 1.49 × [tex]10^{-9}[/tex] C²
and
we have Q2 = 93 ×[tex]10^{-6}[/tex] C - Q1
put here value
Q1² - 93 ×[tex]10^{-6}[/tex] Q1 + 1.49 × [tex]10^{-9}[/tex] = 0
solve we get
Q1 = 2.06 ×[tex]10^{-5}[/tex] C
and
Q1Q2 = 1.49 × [tex]10^{-9}[/tex]
2.06 ×[tex]10^{-5}[/tex] Q2 = 1.49 × [tex]10^{-9}[/tex]
Q2 = 7.23 × [tex]10^{-5}[/tex] C
and
if force is attractive we get here
Q1Q2 = - 1.49 × [tex]10^{-9}[/tex] C²
then
Q1² - 93 ×[tex]10^{-6}[/tex] Q1 - 1.49 × [tex]10^{-9}[/tex] = 0
we get here
Q1 = 1.07 × [tex]10^{-4}[/tex] C
and
Q1Q2 = - 1.49 × [tex]10^{-9}[/tex]
2.06 ×[tex]10^{-5}[/tex] Q2 = - 1.49 × [tex]10^{-9}[/tex]
Q2 = -1.39 × [tex]10^{-5}[/tex] C
The charge when the force is repulsive [tex]q_2 = 7.23*10^-^5C[/tex] and when the force were attractive, the charge is [tex]q_2 = -1.39*10^-^5C[/tex]
Data;
- Total charge = 93.0μC
- distance apart = 1.14m
- Force = 10.3N
Coulomb's Law
This states that the force between two charges is directly proportional to it and inversely proportional to it's square root of distance apart.
[tex]F = \frac{kQ_1Q_2}{r^2} \\Q_1Q_2 = \frac{Fr^2}{k} = 1.49*10^-9C^2[/tex]
The second charge q2 is
[tex]q_2 = 93.0*10^-6 - q_1\\[/tex]
substituting the values to give an equation,
[tex]q_1^2 - 93.0*10^-6q_1 + 1.49*10^-9 = 0\\[/tex]
Let's solve the quadratic equation
[tex]q_1 = 2.06*10^-^5C\\q_2 = \frac{1.49*10^-^9}{q_1} \\q_2 = 7.23*10^-^5C[/tex]
b) When the force is attractive
[tex]q_1q_2 = -1.49*10^-^9C^2\\q_1^2 - 93.0*10^-6q_1 - 1.49*10^-^9 = 0\\q_1 = 1.07*10^-^4C\\q_2 = \frac{-1.49*10^-^9}{q_1} = -1.39*10^-^5C[/tex]
The charge when the force is repulsive [tex]q_2 = 7.23*10^-^5C[/tex] and when the force were attractive, the charge is [tex]q_2 = -1.39*10^-^5C[/tex]
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