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(A) The potential $V$ of a spherical conductor of radius $r$ carrying a charge $q$ is given by $V = \frac{k q}{r}$,where $k$ is the electrostatic cons

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(A) The potential $V$ of a spherical conductor of radius $r$ carrying a charge $q$ is given by $V = \frac{k q}{r}$,where $k$ is the electrostatic constant.Since the charge is added one electron at a time,the total charge $q$ on the particle is quantized,i.e.,$q = n e$,where $n$ is an integer and $e$ is the elementary charge.Substituting $q = n e$ into the potential formula,we get $V = \frac{k (n e)}{r}$.This shows that the potential $V$ increases in discrete steps as each electron is added to the particle.Therefore,the graph of the total charge $q$ versus the applied voltage $V$ will be a step function,where the charge remains constant at each integer multiple of $e$ for a specific range of potential,and then jumps to the next level as the next electron is added.

$A$ neutral spherical copper particle has a radius of $10 \,nm$ $(1 \,nm = 10^{-9} \,m)$. It gets charged by applying the voltage,slowly adding one electron at a time. Then,the graph of the total charge on the particle versus the applied voltage would look like:

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