Physics, 06.10.2019 00:30 Flamingmaster99

Two positive point charges are a fixed distance apart. the sum of their charges is qt. what charge must each have in order to maximize the electric force between them.

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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 moreLearn more about point charges Learn more about the electric force Learn more about fixed distance apart Answer details

Grade: 9

Subject: physics

Chapter: the electric force

Keywords: point charges, the electric force, fixed distance apart, charge, force

Answer from: Quest

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thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.

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How does a pendulum model an energy conversation system?

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Two positive point charges are a fixed distance apart. the sum of their charges is qt. what charge m...