A thin metallic spherical shell of radius R carries a charge Q on… - Vidyadip

Question

A thin metallic spherical shell of radius R carries a charge Q on its surface. A point charge Q/2 is placed at the centre C, and another charge + 2Q is placed outside the shell at A at a distance x from the centre as shown in the figure.

Find the electric flux through the shell.
State the law used.
Find the force on the charges at the centre C of the shell and at the point A.

✓

Answer

Electric flux through a Gaussian surface,

$\varphi = \frac{\text{total enclosed charge }}{\in_{0}}$

Net charge enclosed inside the shell q = 0

$\therefore$ Electric flux through the shell $\frac{\text{q}}{\in_{o}} = 0 $

even when the student writes - Electric flux through the shell is zero as electric field inside the shell is zero.

Gauss Law - Electric flux through a Gaussian surface is ¹/∈₀ times the net charge enclosed within it.

Alternate Answer

$\oint\overrightarrow{\text{E}}.\overrightarrow{\text{d}S} = \frac{\text{q}}{\text{E}_{o}}$

Force on the charge at the centre i.e. Charges ^𝑄/2 =0

$\text{F}_{A} = \frac{1}{4\pi\text{E}_{o}}\frac{2\text{Q}(\text{Q} + \text{Q} / 2)}{\text{x}^{2}}$

$ = \frac{1}{4\pi\text{E}_{o}}\frac{3\text{Q}^{2}}{\text{x}^{2}}$.

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