Solving Two Identical Conduction Spheres Problem

AI Thread Summary
To solve the problem involving two identical conduction spheres, the electrostatic force between them can be calculated using Coulomb's law. After connecting the spheres with a conducting wire, the charges will redistribute until they reach equilibrium, resulting in both spheres having the same net charge. The average of the two initial charges must be calculated, taking into account their signs, to determine the new charge on each sphere. The same Coulomb's law equation can be applied to find the electrostatic force after equilibrium is reached. Understanding the charge redistribution is crucial for solving part b) of the problem effectively.
AznBoi
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Homework Statement


Two identical conduction spheres are placed with their centers 0.30m apart. One is given a charge of 12 x 10 ^-9 C, the other a charge of -18 x 10 ^-9 C a) Find the electrostatic force exerted on one sphere by the other. b) The spheres are connected by a conducting wire. Find the electrostatic force between the two after equilibrium is reached.

Homework Equations


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

The Attempt at a Solution


I already solved a). It was really easy because all I did was plug in the correct information with the correct variables and solved for the electrostatic force between the objects.

How in the world do you start part b)?? Equilibrium means that the net force (F) will equal zero right? However, that isn't true because there is a force in the answer key. Mabye I'm thinking about the motion force and not the electrostatic force. Is there always a consistent electrostatic force?

Please. Can someone help me start part b) of the problem? I'm clueless here. Do you still use the same equation? I know that you can never just keep plugging in numbers to solve for these problems lol. I want to understand the concepts as well. Thanks! :smile:
 
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note when there is a conducting wire connecting the two sphere... charges will re-distribute themselves so that both spheres carry the same net charge...
 
Does that mean I have to find the average of the two charges and then plug them into the equation? If I find the average, do I use the absolute value of the charges or do I include any negative signs?
 
AznBoi said:
Does that mean I have to find the average of the two charges and then plug them into the equation? If I find the average, do I use the absolute value of the charges or do I include any negative signs?

Can someone please tell me if the above procedure will work? I know for a fact that the electrons (charges) are distributed evenly. How should one do this? My method is quoted above. Will it work? Thanks.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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