A metal sphere of radius 10 cm is charged up to a potential of 80 esu. After sharing its chage with another sphere, the common potential of them becomes 20 esu. What is the radius of the second sphere ?

Explanation

Radius of the first sphere = 10 cm
Capacitance `C_1 = 10 `statF and potential, `V_1 = 80` statV
Charge, `Q_1= C_1V_1 = 10xx 80 = 800` statC
After connection, the common potential, V = 20 statV
`V =(" total charge of the two spheres ")/(" equivalent capacitance of the two spheres ")`
or, `20 = (800)/(10+C_2) [ C_2 = " capacitance of the second sphere "]`
or, `10+C_2 = 40" or " C_2 = 30` statF
Radius of the second sphere = 30 cm.