Answer:
Step-by-step explanation:
Since the spherical shell has a net charge of -2 µC, it will create an electric field outside the shell. Within the shell, the electric field is zero due to symmetry.
a) To find the electric field 0.1 m from the center, we can use Gauss's law and consider a Gaussian surface in the shape of a sphere with a radius of 0.1 m centered at the center of the spherical shell. The electric field at a distance r from the center of the spherical shell is given by:
E = kq / r^2
where k is Coulomb's constant (9.0 x 10^9 N*m^2/C^2) and q is the charge enclosed by the Gaussian surface.
In this case, the charge enclosed by the Gaussian surface is the point charge of +2 µC at the center of the spherical shell. Therefore, we have:
E = kq / r^2 = (9.0 x 10^9 N*m^2/C^2) * (2 x 10^-6 C) / (0.1 m)^2 = 1.8 x 10^6 N/C
So the electric field 0.1 m from the center is 1.8 x 10^6 N/C.
b) To find the electric field 0.5 m from the center, we can again use Gauss's law and consider a Gaussian surface in the shape of a sphere with a radius of 0.5 m centered at the center of the spherical shell. The charge enclosed by this Gaussian surface is the sum of the point charge of +2 µC at the center and the charge of -2 µC on the spherical shell. Therefore, we have:
q_enclosed = q_center + q_shell = 2 x 10^-6 C - 2 x 10^-6 C = 0 C
Since there is no charge enclosed by the Gaussian surface, the electric field at a distance of 0.5 m from the center is zero.
So the electric field 0.5 m from the center is 0 N/C.