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? asked in Science & MathematicsPhysics · 9 years ago

How many electrons would one grain have to pick up?

Much of the material making up Saturn's rings is in the form of tiny dust grains having radii on the order of 10^-6 m. These grains are located in a region containing a dilute ionized gas, and they pick up excess electrons. As an approximation, sup-pose each grain is spherical, with radius R=1.0x10^-6 m. How many electrons would one grain have to pick up to have a poten-tial of -400 V on its surface (taking V=0 at infinity)?

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  • 9 years ago
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    V = k*Q / R

    So the required charge is

    Q = V * R / k = -400 * 10^-6 / 9*10^9 = -4.4*10^-14 Coulomb

    The number of electrons is N = Q / e

    N = -4.4*10^-14 / -1.6*10^-19 = 278,000

    or about 300,000 to 1 sig.fig.

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