MCQ
A solid metallic sphere has a charge $ + \,3Q$. Concentric with this sphere is a conducting spherical shell having charge $ - Q$. The radius of the sphere is $a$ and that of the spherical shell is $b(b > a)$. What is the electric field at a distance $R(a < R < b)$ from the centre
  • A
    $\frac{Q}{{2\pi {\varepsilon _0}R}}$
  • B
    $\frac{{3Q}}{{2\pi {\varepsilon _0}R}}$
  • $\frac{{3Q}}{{4\pi {\varepsilon _0}{R^2}}}$
  • D
    $\frac{{4Q}}{{4\pi {\varepsilon _0}{R^2}}}$

Answer

Correct option: C.
$\frac{{3Q}}{{4\pi {\varepsilon _0}{R^2}}}$
c
(c) Electric field at a distance $R$ is only due to sphere because electric field due to shell inside it is always zero. Hence electric field =$\frac{1}{{4\pi {\varepsilon _0}}}.\frac{{3Q}}{{{R^2}}}$

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