The potential of the first sphere before after contact is:
φ1′=4πε01R1q1′ where q1′ is the charge on the first sphere after contact and R1 is the radius of the first sphere.
The potential of the second sphere after contact is:
φ2′=4πε01R2q2′ where q2′ is the charge on the second sphere after contact and R2 is the radius of the second sphere.
As far as the charge conserves, the total anoum of charge will not change:
q1′+q2′=4μC+(−6μC)=−2μC
After contact the potentials of the spheres will be equal to each other:
φ1′=φ2′⇒R1q1′=R2q2′ Express q1′ and substitute it to the previous equation:
q1′=q2′R2R1q2′R2R1+q2′=−2μCq2′=−2R1+R2R2μC The charge of the first sphere will be:
q1′=−2R1+R2R1μC
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