How Does Charge Distribution Affect Electrostatic Energy and Potential?

AI Thread Summary
The discussion revolves around calculating electrostatic energy and potential in systems with multiple charges and conducting spheres. The first problem involves four charges at the corners of a square, yielding an electrostatic energy of -4.7 J. The second problem compares the potentials of two conducting spheres, with the smaller sphere at 100V, while the potential of the larger sphere is debated among several options. The third problem involves three connected conducting spheres, where the charge on the large sphere in equilibrium is determined to be 2.0 x 10^-4 C. Participants express confusion over their calculations and the use of combinations in solving these electrostatic problems.
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1. Four charges are placed at the corners of the square where the opp diagonals have +2microcoulombs and -2 coulombs. what is the electrostatic energy of the system? ANS: -4.7 J


2. Two conducting spheres that carry equal charges are very far from each other and from all other charges. One of these spheres has twice the radius of the other one. If the potential of the smaller sphere (relative to infinity) is 100V, the potential of the arger sphere (relative to infinity) is closest to... ANS: 100V, 200V, 50V, 25V, or 400V

3. three conducting spheres of radii 1m, 2m and 3m are connected by wires 50 meters long in a triangle with the angles 60 degrees each. a charge of 4x10^-4 C is initially placed on teh large sphere. determine the charge on teh large sphere in equilibrium. ANS 2.0 x 10^-4






The attempt at a solution
1) I tried using PE = kq1q1/R... found the sides and the diagonals but I got an answer of zero, which is wrong.

2) I found the net energy of both spheres, and then used this energy with the given potential to find the potential of the larger sphere, but i think I am rearranging wrong?

3) i drew a FBD diagram and did horizontal and vertical components on teh larger sphere, but I got a much larger number as my answer.

 
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You will have 4C2 combinations to consider.
Two of these will be diagonally opposite pairs and all others will be adjacent pairs.
 
I have no idea why you would use combinations for my problems
 
Was just telling you there would be 6 pairs to consider.
 
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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