CBSE Class 12 · 2012 · ElectrostaticsLong Answer

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(a) Define electric flux. Write the S.I. units. (b) Using Gauss's law, prove that the electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it. (c) How is the field directed if (i) the sheet is positively charged, (ii) negatively charged?

Solution

(a) Electric flux:

ϕ = E \cdot Δ S, S.I. unit N m^{2} C^{- 1}

(b) Take a pillbox of face area

A

piercing the sheet symmetrically; the field is normal and equal on both faces:

2 E A = \frac{σ A}{ε _{0}}

E = \frac{σ}{2 ε _{0}}

This contains no

r

, so the field is the same at all distances.
(c)(i) For positive

σ

the field points away from the sheet; (ii) for negative

σ

, towards it.

CBSE Class 12 Board · 2012 · Subjective

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