Question

A spherical surface completely surrounds a collection of charges. Find the electric flux through the surface if the collection consists of the following charges. (a) a single +4.10 10-6 C charge (b) a single -2.20 10-6 C charge (c) both of the charges in (a) and (b)

Answer 1

apply electric flux phi = Q/eo     Gauss law

a. when q = 4.1 e-6

fluxc = 4.1 e-6/(8.85e-12)

fluxc = 4.63 *10^5 Nm^2/C

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when Q = -2.2 e-6

flucx = 2.2 e-6/8.85e-12

flux   = 2.48 *10^5

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when both charge

Qnet = 4.1-2.2 = 1.9 e-6

so flux   = 1.9 e-6/(8.85e-12)

flux = 2.14 *10^5 Nm^2/C

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Answer 2

Gauss's law may be used

$\Phi_E = \frac{Q}{\varepsilon_0}$

where ?_E is the electric flux through a closed surface S enclosing any volume V, Q is the total charge enclosed within S, and ?₀ is the electric constant.

then ,

a) flux = 4.10 10^-6 C/ ?₀

Flux = 4.63*10⁵ N.m^2/C

b)

flux = -2.2 10^-6 C/ ?₀

Flux = -2.48*10⁵ N.m^2/C

c)

flux =(4.1 -2.2) 10^-6 C/ ?₀

Flux = 2.15*10⁵ N.m^2/C

Answer 3

flux=Q/e₀

(a)

Flux=4 x 10-6/8.85x10^-12=4.52x10⁵Vm

(b)

Flux=2.2 x 10-6/8.85x10^-12=2.49x10⁵Vm

(c)

Q=4-2.2=1.8x10^-6C

Flux=1.8 x 10-6/8.85x10^-12=2.03x10⁵Vm