Question

Suppose you have a total charge qtot that you can split in any manner. Once split, the separation distance is fixed. How do you split the charge to achieve the greatest force

Answer 1

To achieve the greatest force, split the charge in a way that maximizes the repulsive force between the charges. This can be done by splitting the charge into two equal charges with the same sign placed as close together as possible.

Step-by-step explanation:

To achieve the greatest force, you should split the charge in a way that maximizes the repulsive force between the charges. According to Coulomb's law, the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the separation distance.

Therefore, to maximize the force, you should split the charge in such a way that the individual charges have the same sign (either positive or negative) and are placed as close together as possible. This will result in a large repulsive force between the charges.

For example, if you have a total charge of qtot, you can split it into two equal charges, q/2 and q/2, placed at a distance d from each other. This will result in a large repulsive force between the charges.

Answer 2

Answer is explained in the explanation section below.

Step-by-step explanation:

Solution:

We know from the Coulomb's Law that, Coulomb's force is directly proportional to the product of two charges q1 and q2 and inversely proportional to the square of the radius between them.

So,

F =
`(Kq1q2)/(r^(2) )`

Now, we are asked to get the greatest force. So, in order to do that, product of the charges must be greatest because the force and product of charges are directly proportional.

Let's suppose, q1 = q

So,

if q1 = q

then

q2 = Q-q

Product of Charges = q1 x q2

Now, it is:

Product of Charges = q x (Q-q)

So,

Product of Charges = qQ -
`q^(2)`

And the expression qQ -
`q^(2)` is clearly a quadratic expression. And clearly its roots are 0 and Q.

So, the highest value of the quadratic equation will be surely at mid-point between the two roots 0 and Q.

So, the midpoint is:

q =
`(Q + 0)/(2)`

q = Q/2 and it is the highest value of each charge in order to get the greatest force.