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Alternating Current — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsAlternating Current3 Marks
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.
  1. Find the electric flux through the shell.
  2. State the law used.
  3. Find the force on the charges at the centre C of the shell and at the point A.

✓

Answer

  1. 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.

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

Alternate Answer

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

  1. 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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