A thin metallic spherical shell of radius 50 cm has a total charge of 4.0 µC placed on it. At the center of the shell is placed a point charge of 2.00 µC. What is the electric field at a distance of 30.0 cm from the center of the spherical shell? A) 6.0 × 10⁵ N/C outward B) 2.0 × 10⁵ N/C outward C) 4.0 × 10⁵ N/C inward D) 4.0 × 10⁵ N/C outward E) 0.0

Question

Quizplus · Accepted Answer

According to Gauss's Law, the electric field at a distance outside of a charged spherical shell is the same as if all of the charge were concentrated at the center of the shell. Therefore, the electric field at a distance of 30.0 cm from the center of the spherical shell is the same as the electric field created by a point charge of 2.00 µC at the center of a sphere with a radius of 30.0 cm. Using Coulomb's Law, we can determine that the magnitude of the electric field is:
E = k*(q/r^2) = (9.0 x 10^9 N*m^2/C^2)*(2.00 x 10^-6 C)/(0.30 m)^2 = 2.0 x 10^10 N/C
The direction of the electric field is outward from the center of the sphere, since the point charge is positive. Therefore, the final answer is choice B.

A Thin Metallic Spherical Shell of Radius 50 Cm Has