Coulomb's Law and electrostatic force

[SAGHTD]

Homework Statement

Of the charge 'Q' initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. Both spheres can be treated as particles. For what value of q/Q will the electrostatic force between the two spheres be maximized?

The Attempt at a Solution

The theory in this topic is giving me a little problems. i just would like to know if I'm on the correct path of thinking and working the question out.

I understand electrostatic forces either repels or attractions. Now as the questions asked for the max value for the electrostatic. i think for the max value for electrostatic force between the two particles, the charge between the two spheres must have a even distribution of charge i guess. Like the charge on particle 1 could be +5 and charge on particle 2 is also +5 but what about the if the the charge on particle 1 is greater than that of particle 2 would the force be greater? am i doing this question correct or you have to use an equation of something??

 

[cepheid]

or you have to use an equation of something??

Yes, you have to use Coulomb's law, which expresses the mutual force of attraction (or repulsion) between two charges.

If the amount transferred to the second sphere is q, then the amount of charge left on the first sphere is (Q-q). So, use coulomb's law with Q₁ = (Q-q) and Q₂ = q.

You can then differentiate the expression w.r.t. q and set the result equal to zero to find the minimum.

 

[cupid.callin]

You can then differentiate the expression w.r.t. q and set the result equal to zero to find the minimum.

He needs maximum force not minimum! Minimum force will be at q=0.

But yes your method is correct.

 

[cepheid]

He needs maximum force not minimum! Minimum force will be at q=0.

But yes your method is correct.

Yeah, good catch. The wording is wrong. However, differentiating will naturally lead to a maximum.

 

[rwisz]

I can confirm that your understanding of electrostatic forces is correct. Coulomb's Law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Therefore, for the electrostatic force to be maximized, the charges on both particles should be at their maximum value and the distance between them should be minimized.

In this case, the charge 'Q' initially on the tiny sphere represents the maximum charge that can be transferred. So, the value of q should be equal to Q in order to maximize the electrostatic force between the two spheres. This means that the charge should be evenly distributed between the two spheres, as you correctly stated.

To calculate the exact value of q/Q, we can use the equation for Coulomb's Law:

F = k * (q1 * q2) / r^2

Where:
F = electrostatic force
k = Coulomb's constant
q1 and q2 = charges on the two particles
r = distance between the two particles

Since we want to maximize the force, we can set the distance between the two particles to be very small (r = 0). This means that the value of q/Q will be equal to the maximum value of the force (Fmax).

Therefore, q/Q = Fmax / (k * Q^2).

I hope this helps you to understand the topic better and solve the problem correctly. Keep up the good work in your studies!