A conductive sphere of radius r is given a charge Q. Another sphere of radius R is put in contact with it.They are separated after they have shared a charge. assuming that the spheres are held at fixed distance apart, what should be the value of R so that the force between two charged spheres is the maximum?..if u can help me out!

Dear Student,

Please find below the solution to the asked query:

Potential of the first sphere and second sphere after the charge distribution are,

V1=14πε0Q1r and V2=14πε0Q2R

When these two spheres are kept in contact, then the potential of the two spheres should be same. Therefore,

V1=V2  14πε0Q1r=14πε0Q2R  Q1=rRQ2

The total charge will be 

Q1+Q2=Q  Q2rR+1=Q  Q2=RR+rQ Q1=rR+rQ

Therefore, when the two charges are placed at a distance "d", then the force of repulsion between them is,

F=14πε0Q1Q2d2= 14πε01d2rr+RRr+RQ2 F=14πε0Q2d2rRr+R2For F to be maximum dFdR=0 dFdR=ddR14πε0Q2d2rRr+R2=0 r+R2r+rR2r+Rr+R4=0  r+R2r+rR2r+R=0 r+R+2R=0  3R=r R=r3


Hope this information will clear your doubts about the topic.

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