A solid sphere of radius a is concentric with a hollow sphere of radius b, where b a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r

Question

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r < a, is which of the following, in terms of k = 4π₀)^-¹?

Quizplus · Accepted Answer

By Gauss's law, since the electric field is a conservative field, it is determined uniquely by the total charge enclosed within the Gaussian surface. For any radius r < a, the Gaussian surface completely encloses the solid sphere, which has a charge of +Q. Since the hollow sphere is concentric with the solid sphere, it does not contribute to the electric field at this radius. Therefore, the total charge enclosed is +Q, and Gauss's law gives us:

∫E·dA = Q/ε0

E·4πr^2 = Q/ε0

E = Q/(4πε0r^2)

which shows that the electric field at radius r is inversely proportional to r^2, and thus it approaches infinity as r approaches zero. However, this calculation does not depend on the charge on the hollow sphere, which is irrelevant for calculating the electric field at this radius. Therefore, the electric field at radius r is independent of the charge on the hollow sphere, and is given by choice E, which is zero.

A Solid Sphere of Radius a Is Concentric with a Hollow