Answer:
A) and B) the electric field is 0
C) E = - 28266.88 [N/C]
D) The electric field is inward the sphere
E) E = 18463,47 [N/C]
F)The electric field is outwad th sphere
Explanation:
A) At point 4 cm from the center, strength of the electric field is 0.
If we imagine a gaussian sphere of radius 4 it wont enclose any net charge
B) There is not electric field at radius r = 4 cm
C) We first compute the whole charge in the surface of the sphere of radius r = 7 cm
A = 4π* r² ⇒ A = 4* 3,14 * ( 0,07 m)² ⇒ A = 0.615 m²
And total charge of the inside sphere is
Q = -300 * 10⁻⁹ * 0.615 [C] ⇒ Q = - 18,46 *10⁻⁹ [C]
Then if we again imagine a gaussian sphere passing through a point at 8 cm from the center the enclosed charge will be Q, and the strength of the electric field in that point is
E = - K * 18.46* 10⁻⁹ [C]/ (0.08)² m² ⇒ E = - K * 2884.38*10⁻⁹ [C/m²]
K = 9.8 *10⁹ [Nm²/C² ] and E = - 9.8* 2884.38 [N/C]
E = - 28266.88 [N/C]
D) The negative sign indicates that the electric field is inward
E) We need to compute total charge in the outside surface of the bigger shell
Q = 300*10⁻⁹ [C] and the area of the shell is
A = 4*π * (0.11)² m² ⇒ A = 0, 1519m²
Q₂ = 300 * 10⁻⁹ * 0,1519 [C] Q₂ = 45,59 * 10⁻⁹ [C]
The net charge enclosed for a gaussian surface passing through point at 12 cm from the center is:
Q₂ - Q = + 45.59* 10⁻⁹ - 18.46 * 10⁻⁹ Q(t) = 27,13* 10⁻⁹ [C]
and the strength of the electric field in that point is
E = K * 27,13* 10⁻⁹ / (0,12)² E = 9.8 *27,13/ 0,0144 [N/C]
E = 18463,47 [N/C]
And as total net charge is positive the electric field is outward the sphere
