Answer to Question #7986 in Electromagnetism for wes edwards
and E be
the electric dield at some point of S.
Due to symmetricity of the ball and
sphere the absolute value of E is the same at all points of S.
vector E is parallel to normal vector to S.
Hence the flux Phi through S is
Phi = integral_over_S (E dA) = E * Area_of_S = E * 4 pi *
On the other hand, due to Gauss' law
Phi is equal to the full
charge Q inside S divided by eps_0:
Phi = Q/eps_0.
The ball is
uniformly charged, so
Q = p * Volume_of_a_ball = p * 4/3 * pi *
Phi = E * 4 pi * d^2 = p * 4/3 * pi * a^3 /
E = (p * 4/3 * pi * a^3) / (4 pi * d^2 * eps_0
= a^3 * p / (3 * eps_0 * d^2)
Answer: E = a^3 * p / (3 *
eps_0 * d^2)
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