Physics

Physics

Problem

59. 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\mathrm{V}=\mathrm{kq} / \mathrm{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? A) W=kQ/RW=k Q / R B) W=kQ2/RW=k Q^{2} / R C) W=∫0Q(kq/R)dq\mathrm{W}=\int_{0}^{Q}(k q / R) d q D) W=∫0Q(kq2/R)dq\mathrm{W}=\int_{0}^{Q}\left(k q^{2} / R\right) d q E) W=∫0Q(kq/R2)dq\mathrm{W}=\int_{0}^{Q}\left(k q / R^{2}\right) d q C) W=∫0Q(kq/R)dq\mathrm{W}=\int_{0}^{Q}(k q / R) d q D) W=∫0Q(kq2/R)dq\mathrm{W}=\int_{0}^{Q}\left(k q^{2} / R\right) d q E) W=∫0Q(kq/R2)dq\mathrm{W}=\int_{0}^{Q}\left(k q / R^{2}\right) d q

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