Question
A hollow insulated conducting sphere is given a positive charge of $$10\,\mu C.$$ What will be the electric field at the centre of the sphere if its radius is $$2\,m$$ ?
A.
Zero
B.
$$5\,\mu C{m^{ - 2}}$$
C.
$$20\,\mu C{m^{ - 2}}$$
D.
$$8\,\mu C{m^{ - 2}}$$
Answer :
Zero
Solution :
Charge resides on the outer surface of a conducting hollow or solid sphere of radius $$R$$ (say). We consider a spherical surface of radius $$r < R.$$
By Gauss’ theorem, $$\sum {E \cdot ds = \frac{{{q_{{\text{inside}}}}}}{{{\varepsilon _0}}}} $$
or $$E \times 4\pi {r^2} = \frac{1}{{{\varepsilon _0}}} \times {q_{{\text{inside}}}}$$
and we know that $${q_{{\text{inside}}}} = 0$$
So, $$E = 0$$
i.e. electric field inside a hollow sphere is zero.
Charge resides on the outer surface of a conducting hollow or solid sphere of radius $$R$$ (say). We consider a spherical surface of radius $$r < R.$$
By Gauss’ theorem, $$\sum {E \cdot ds = \frac{{{q_{{\text{inside}}}}}}{{{\varepsilon _0}}}} $$
or $$E \times 4\pi {r^2} = \frac{1}{{{\varepsilon _0}}} \times {q_{{\text{inside}}}}$$
and we know that $${q_{{\text{inside}}}} = 0$$
So, $$E = 0$$
i.e. electric field inside a hollow sphere is zero.
