Question

Gauss' theorem states that total normal electric induction over a closed surface in an electric field is equal to ________. a.1/r
b.1/r^2.
c. 1/r^3.
d.r^3
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Answer 1

Answer:1/r^3

Explanation:

Answer 2

Gauss' theorem states total normal electric induction over a closed surface in an electric field is proportional to 1/r (a).

1) The above expression can be derived as follows:

(TNEI) ds = ε0 * k *(q / 4 *Pi* ε0 * k r) * cos ( theta) ds

2) (TNEI) ds = ( q / 4 * Pi ) * (ds cos(theta)/ r^2)

3) But ds cos(theta)/ r^2 = dw

4)dw = solid angle subtended by area ds.

5) So, substituting we get, (TNEI) ds = (q / r * pi) dw