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 \(\frac{Q_T}{2}\)
Further explanation
The electric force is directly proportional to the amount of charge (\(q_1\) and \(q_2\)) and inversely proportional to the distance between the charges r.
The sum of the two charges is \(q_1 + q_2\)
\(Q_T\), let
\(q_1 = q\) then \(q_2 = Q_T - q\)
Then the force between two charges is given by the formula
\(F = \frac{1}{4 \Pi \epsilon_0} \frac{q_1 q_2}{r^2}\)
Therefore the force is
\(F = \frac{1}{4 \Pi \epsilon_0} \frac{q*(Q_T - q)}{r^2}\)
a. given that the distance between the two charges is fixed. To get the maximum force the condition is
\(\frac{dF}{dq} = 0\), where
\(\frac{1}{4 \pi \epsilon_0}, r^2\) are constants
Now,
\(\frac{d}{dq} (qQ_T -q^2 ) = 0\)
Where
\(Q_T - 2q = 0\\\q = \frac{Q_T}{2}\)
The force between the two charges is maximum only when
\(q_1 = q = \frac{Q_T}{2}, q_2 = Q_T - q = Q_T - \frac{Q_T}{2} = \frac{Q_2}{2}\)
So if the two charges have the value \(\frac{Q_T}{2}\) 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
