Question

One of the hazards facing humans in space is space radiation: high-energy charged particles emitted by the sun. During a solar flare, the intensity of this radiation can reach lethal levels. One proposed method of protection for astronauts on the surface of the moon or Mars is an array of large, electrically charged spheres placed high above areas where people live and work. The spheres would produce a strong electric field \underset{E}{\rightarrow} to deflect the charged particles that make up space radiation. The spheres would be similar in construction to a Mylar balloon, with a thin, electrically conducting layer on the outside surface on which a net positive or negative charge would be placed. A typical sphere might be 5 m in diameter. Suppose that to repel electrons in the radiation from a solar flare, each sphere must produce an electric field \underset{E}{\rightarrow} of magnitude 1 × 106 N/C at 25 m from the center of the sphere.What is the magnitude of E⃗ just outside the surface of such a sphere?a) 0b) 106 N/Cc) 107 N/Cd) 108 N/C

Answer 1

Answer:

c) The magnitud of field is 10⁷ N/C

Explanation:

An easy way to solve this exercise is by using Gauss's law

           Ф = ∫ E .dA = $q_{int}$ / ε₀

As the balls are spherical we create a spherical Gaussian surface, in this case the electric field line for letter radii of the sphere and the scaled product is reduced to the ordinary product

        E A =  $q_{int}$ / ε₀

The area of ​​a sphere is

        A = 4π R²

        $q_{int}$ = E 4π R² ε₀

Let's calculate the charge on the ball

       $q_{int}$ = 1.0 10⁶ 4π 25²2 8.85 10⁻¹²

      $q_{int}$ = 6.95 10⁻² C

Now we can calculate the taste load outside the surface of the globe R = 5 m

     E =  $q_{int}$ / A ε₀

     E =  $q_{int}$ / (4π R² ε₀)

     E = 6.95 10⁻² / (4π 5²  8.85 10⁻¹²)

     E = 2.5 10⁷ C / m

The magnitud of field is 10⁷ N/C