A solid conducting sphere of radius r_a is placed concentrically inside a conducting spherical shell of inner radius r_b1 and outer radius r_b2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge. The electric field for r r_b1 is

Question

A solid conducting sphere of radius r_a is placed concentrically inside a conducting spherical shell of inner radius r_b1 and outer radius r_b2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge. The electric field for r > r_b1 is

Quizplus · Accepted Answer

The electric field inside a conductor is zero, so the electric field from the inner sphere will only contribute to the electric field for $r>r_{b}$ (outside the conducting shell). For $r>r_{b}$, the electric field will be the same as that of a point charge $Q$ at the origin, so the electric field is given by:
$$
E=\frac{kQ}{r^{2}}
$$
where $r$ is the distance from the origin. Therefore, the electric field for $r>r_{b}$ is:
$$
E=\frac{kQ}{r^{2}}=\frac{kQ}{r_{b}^{2}}\cdot\frac{r_{b}^{2}}{r^{2}}=\frac{kQ}{r_{b}^{2}}\cdot\frac{r_{b}}{r}\cdot\frac{r_{b}}{r}=\frac{kQ}{r_{b}^{2}}\cdot\left(\frac{r_{b}}{r}\right)^{2}
$$
Since $r_{b}$ is the inner radius of the conducting shell, we have $r_{b}>r_{s}$, where $r_{s}$ is the radius of the inner sphere. Therefore, the electric field is non-zero for $r>r_{s}$, so choice B is correct.

A Solid Conducting Sphere of Radius Ra Is Placed Concentrically

A Solid Conducting Sphere of Radius R_a Is Placed Concentrically