A particle carrying charge +q is placed at the center of a thick-walled conducting shell that has inner radius R and outer radius 2R and car

Question

A particle carrying charge +q is placed at the center of a thick-walled conducting shell that has inner radius R and outer radius 2R and carries charge −2q. A thin-walled conducting shell of radius 5R carries charge +2q and is concentric with the thick-walled shell. Define V = 0 at infinity. Calculate all distances from the particle at which the electrostatic potential is zero.

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Linh Đan 3 years 2021-07-25T15:20:30+00:00 1 Answers 19 views 0

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  1. Calantha
    0
    2021-07-25T15:22:21+00:00
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    Answer:

    10R/11 and 5R/2

    Explanation:

    The radius of the conducting shell = R,

    Electrostatic potential inside the shell (r<R) = kq/R

    Electrostatic potential outside the shell (r>R) = kq/r

    If x is the point of zero potential

    Electrostatic potential for inner shell, V_{1} = \frac{kq}{X - R}

    Electrostatic potential for outer shell, V_{2} = \frac{-2kq}{X - 2R}

    Electrostatic potential for the thin walled shell, V_{3} = \frac{2kq}{X - 5R}

    V_{1} + V_{2} + V_{3} = 0

    \frac{kq}{X-R} - \frac{2kq}{X-2R} + \frac{2kq}{X-5R} = 0

    \frac{1}{X-R} - \frac{2}{X-2R} + \frac{2}{X-5R} = 0\\(X-R) - 2(X-R)(X-5R)+2(X-R)(X-2R) = 0

    The values of X=r that satisfy the above equation are 10R/11 and 5R/2

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