Chapter 23, Problem 15 from Physics for Scientists and Engineerswith Modern Phys

Question

Chapter 23, Problem 15 from Physics for Scientists and Engineerswith Modern Physics (4th) I need help with this problem. hereit is
An insulated spherical conductor of radius r1 carriesa charge Q. A second conducting sphere of radius r2 and initiallyuncharged is then connected to the first by a long conductingwire.
   A.) After the connection, what can you say about theelectric potential of each sphere?
   B.) How much charge is transferred to the secondsphere? (Assume the connected spheres are far apart compared totheir radii (why make this assumption)

Explanation / Answer

   A.   Electric potential of both the spherewill become same.    B.   Capacitance of conductorof radiusr         C   =   40* r          Hence   C1   =   40* r1                      C2   =   40* r2    Initial potential ofC1         V1   =   Q/ C1                                                  =   Q/ 40 *r1         -----------(1)    Final potential ofC1      Vf1   =   (Q- q) / 40 *r1      -----------(2)    Final potential ofC2      Vf2   =   q/ 40 *r2                     -----------(3)      where q is charge transferredfrom C1 to C2.    Then      Vf1   =   Vf2       (Q - q) /40 *r1   =   q /40 * r2    (Q - q) /r1   =   q /r2    (Q - q) /q   =   r1 /r2    Q /q   -   1   =   r1/ r2    Q /q   =   1   +   r1/ r2    q   =   Q* r2 /(r1   +   r2)    Assumption is to be made so that the chargedistribution and hence potentials are not affected bypolarization.    Assumption is to be made so that the chargedistribution and hence potentials are not affected bypolarization.

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