Respuesta :
Answer:
[tex]E = -9.5\times 10^4~N/C[/tex]
Explanation:
Gauss' Law should be applied to find the E-field 3.9 cm from the surface of the sphere.
In order to apply Gauss' Law, an imaginary spherical shell (Gaussian surface) should be placed around the original sphere. The exact position of the shell must be 3.9 cm from the surface of the original sphere.
Gauss' Law states that
[tex]\int {\vec{E}d\vec{a}} = \frac{Q_{enc}}{\epsilon_0}[/tex]
Here, the integral in the left-hand side is equal to the area of the imaginary surface. After all, the reason behind choosing the imaginary surface a spherical shell is to avoid this integral. The enclosed charge in the right-hand side is equal to the charge of the sphere, -84.0 nC. The radius of the imaginary surface must be 5 + 3.9 = 8.9 cm.
So,
[tex]E4\pi r^2 = \frac{-84\times 10^{-9}}{8.8\times 10^{-12}}\\E4\pi (8.9 \times 10^{-2})^2 = \frac{-84\times 10^{-9}}{8.8\times 10^{-12}}\\\\E = -9.5\times 10^4~N/C[/tex]
