Question

A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre .
(1) increases as r increases for r < R and for r > R
(2) zero as r increases for r < R, decreases as r increases for r > R
(3) zero as r increases for r < R, increases as r increases for r > R
(4) decreases as r increases for r < R and for r > R

Answer 1

Zero as r increases for r < R, decreases as r increases for r > R

Step by step explanation:

Gauss'Law:

According to this law, the net flux through any closed surface equals the total charge inside that surface divided by $\bold{\varepsilon _{o}}$.

                $\bold{\phi _{e}=\oint \overrightarrow{E}.\overrightarrow{dA}=\frac{Q_{net}}{\varepsilon _{o}}}$.....................(1)

Charge Q will be distributed over the surface of hollow metal sphere

Inside ( attachment)

(i)For r < R :

From equation (1),

                     $\bold{\phi _{e}=\oint \overrightarrow{E}.\overrightarrow{dA}=\frac{Q_{net}}{\varepsilon _{o}}=0}$

                         $\Rightarrow E_{in}=0$

(out side)

(ii) For r>R

From equation (1)

                     $\oint \overrightarrow{E_{o}}.\overrightarrow{ds}=\frac{q_{en}}{\varepsilon _{o}}$............................(2)

                     $q_{en}=Q$

Substitute the value  in equation (2)

                    $\Rightarrow E_{o}4\pi r^{2}=\frac{Q}{\varepsilon _{o}}$

                    $\Rightarrow E_{o}\,\alpha \frac{1}{r^{2}}$

Hence, the correct option is 2.

Answer 2

Answer:

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