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A point charge causes an electric flux of –1.0 × 10^3 Nm^2 /C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. What is the value of the point charge?

Q 1.20(b): A point charge causes an electric flux of -1.0\times 10^{3}\frac{Nm^{2}}{C} to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. What is the value of the point charge?

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Given,

\phi = -1.0\times 10^{3}\frac{Nm^{2}}{C}

Using Gauss’s law, we know that the flux of electric field through any closed surface S is 1/\epsilon _{0}  times the total charge enclosed by S.

i.e.   \phi = q/\epsilon _{0}

where, q = net charge enclosed  and  \epsilon _{0} = permittivity of free space (constant)

\therefore q = -10^{3}Nm^2C^{-1} \times 8.85\times10^{-12}N^{-1}m^{-2}C^{2} = -8.8\times10^{-9}\ C \\ = \boldsymbol{-8.8\ nC}

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