A total electric charge of 3.50 nC is distributed uniformly over the surface of a metal sphere with a radius of 24.0 cm. If the potential is

Question

A total electric charge of 3.50 nC is distributed uniformly over the surface of a metal sphere with a radius of 24.0 cm. If the potential is zero at a point at infinity, find the value of the potential at the following distances from the center of the sphere: (a) 48.0 cm; (b) 24.0 cm; (c) 12.0 cm

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RobertKer 5 years 2021-08-05T21:38:01+00:00 1 Answers 638 views 0

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  1. thanhcong
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    2021-08-05T21:39:47+00:00
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    Answer:

    a, V = 65.6V

    b. V = 131.0V

    C. V = 131.0V

    Explanation:

    Given

    Total electric charge q= 3.50nC=3.50\times10^{-9}C distributed  uniform at surface of metal sphere where radius is R = 24cm

    R = 24cm = 0.024m

    we have to find potential at different distance

    a. r = 48cm = 0.048m

    b. r = 24cm = 0.024m

    c. r = 12cm = 0.012m

    a. solution

    Here the distance r is grater then R,we can get the potential outside of sphere

    V = \dfrac{q}{4\pi\varepsilon_0r}

    \textrm{where is} \dfrac{1}{4\pi\varepsilon_0}=9.0\times10^{9}N.m^{2}/c^2

    now we plug the value q and r in potential v

    V=(9\times10^9N.m^2/C^2)\dfrac{3.50\times10^{-9}C}{0.48m}

    =65.6V

    b.solution

    Here distane r is the same from radius R, so we can get potential inside sphere

    v= \dfrac{q}{4\pi\varepsilon_0R}

    Now we plug the value of R and q

    V=(9\times10^9N.m^2/C^2)\dfrac{3.50\times10^{-9}C}{0.24m}

    V=131V

    3.solution

    Inside sphere electric feild is zero.so potential is the same every point inside sphere and equal potential on the surface

    V=131V

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