Two positive point charges are a fixed distance apart. the sum of their charges is qt. The charge that must each have in order to maximize the electric force between them is [tex]\frac{Q_T}{2}[/tex]
Further explanation
The electric force is directly proportional to the amount of charge ([tex]q_1[/tex] and [tex]q_2[/tex]) and inversely proportional to the distance between the charges r.
The sum of the two charges is [tex]q_1 + q_2[/tex]
[tex]Q_T[/tex], let
[tex]q_1 = q[/tex] then [tex]q_2 = Q_T - q[/tex]
Then the force between two charges is given by the formula
[tex]F = \frac{1}{4 \Pi \epsilon_0} \frac{q_1 q_2}{r^2}[/tex]
Therefore the force is
[tex]F = \frac{1}{4 \Pi \epsilon_0} \frac{q*(Q_T - q)}{r^2}[/tex]
a. given that the distance between the two charges is fixed. To get the maximum force the condition is
[tex]\frac{dF}{dq} = 0[/tex], where
[tex]\frac{1}{4 \pi \epsilon_0}, r^2[/tex] are constants
Now,
[tex]\frac{d}{dq} (qQ_T -q^2 ) = 0[/tex]
Where
[tex]Q_T - 2q = 0\\\q = \frac{Q_T}{2}[/tex]
The force between the two charges is maximum only when
[tex]q_1 = q = \frac{Q_T}{2}, q_2 = Q_T - q = Q_T - \frac{Q_T}{2} = \frac{Q_2}{2}[/tex]
So if the two charges have the value [tex]\frac{Q_T}{2}[/tex] then the force is maximum
Learn more
- Learn more about point charges https://brainly.com/question/1969944
- Learn more about the electric force https://brainly.com/question/4593086
- Learn more about fixed distance apart https://brainly.com/question/13134985
Answer details
Grade: 9
Subject: physics
Chapter: the electric force
Keywords: point charges, the electric force, fixed distance apart, charge, force
