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Work in increase charge in a isolated conducting sphere

Physics Asked by Eason Xiao on March 5, 2021

The potential of an isolated conducting sphere of radius R is given as a function of the charge $q$ on the sphere by the equation $V = kq/R$. If the sphere is initially uncharged, the work $W$ required to gradually increase the total charge on the sphere from zero to $Q$ is given by which of the following expressions?

$$W=kQ/R$$

$$W=kQ^2/R$$

$$w=int_0^Qfrac{kq}{R}dq$$

$$w=int_0^Qfrac{kq^2}{R}dq$$

$$w=int_0^Qfrac{kq}{R^2}dq$$

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