Four identical conducting balls, A, B, C and D, are placed on insulating stands.

Question

Four identical conducting balls, A, B, C and D, are placed on insulating stands. Ball A has a net charge of +Q, B has a net charge of -Q and C and D are neutral. Ball C is first brought in contact with ball A and then removed from contact. Then, without discharging Ball C, it is brought in contact with ball B and then removed from contact. What is the final charge state of each ball? Explain your reasoning. If the charged balls are now brought near but not touching each other two by two, and the balls are held the same distance apart in each case, rank the following forces: Explain your reasoning.

Explanation / Answer

.a) electric charges are uniformly distributed in each conductor

when the sphere C touches sphere A + Q charge is distributed evenly between the two spheres, by separating each one it has a charge + Q / 2 the total charge must remain constant

then charged sphere C +Q / 2 playing field B -Q charge some positive charges neutralize negative, are -Q + Q / 2 = -Q / 2 this remaining load is distributed between the two spheres, by separating each one gets half of this burden charge -Q / 4

All in all spheres is with charge

Sphere Charga

A +Q/2

B - Q/4

C - Q/4

D 0

. b)

We assume that we have charge calculated in Part a

Fab = k +Q/2 (-Qa/4)/ r2= k Q2/r2(- ) attraction force directed from B to A

Fbc = k (-Q/4 )(-Q/4)/r2= k Q2/r2( 1/16) repulsive force directed away from C to B

Fad = 0 sphere F is not charge

magnitude of the force is equal

Fab = Fbc

Fbc = Fbc

but the sense of force is reversed

A force is directed from A to B

Fbc force directed from B moving away from C

the Diagram can help you understand this part

-----Fba < ------ Fab

+Qa -Qb

< ----- Fcb Fbc ------ >

-Qb -Qc

Fad = Fda = 0 no force because a sphere has no charge

Another possibility is that the fields have the initial load torque this part, but I think that is the case, you ofall ways we will find the answer

Fab = k +Q (-Q)/ r2 = k Q2/r2

Fbc= 0 sphere C is uncharge

Fad = 0 sphere D is uncharge

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