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Electric Charges and Fields — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsElectric Charges and Fields3 Marks
Question
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude $17.0 \times 10–22 C/m^2$ . What is $E:$
  1. In the outer region of the first plate,
  2. In the outer region of the second plate, and
  3. Between the plates?
✓

Answer

Given, Surface charge density, $\sigma = 17. 0\ x\ 10^{-22}\ C /m^2$
  1. To the left of the plates, electric fields are equal and opposite as plates are close to each other electric field is zero as surface charge density in outer side is zero.
  2. To the right of the plates, electric fields are equal and opposite as plates are close to each other electric field is zero.
  3. Electric fields between the plates are in same direction as total $E.F.$ on both sides of plate due to $\sigma$ surface charge density $= \frac{\sigma}{\epsilon_0}$ electric field of inner side of plate $=\frac{\sigma}{2\epsilon_0}$
and for both plate $E =\frac{\sigma}{2\epsilon_0}+\frac{\sigma}{2\epsilon_0}$
$\text{E}=\frac{\sigma}{\epsilon_0}=\sigma\times4\pi\times9\times10^9$
$E = 17.0 \times 10^{-22} \times 4 \times 3.14 \times 9 \times 10^9$
$E = 1921.7 \times 10^{-13}$
$= 1.92 \times 10^{-10} N/C.$

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