1. State and explain Gauss’s law in electrostatics and use it to determine the electric field intensity due to a line charge.
Ans: Gauss’s Theorem: The total electric flux passing through any closed surface is equal to 1/ϵ0 * net charged enclosed
Ans: Gauss’s Theorem: The total electric flux passing through any closed surface is equal to 1/ϵ0 * net charged enclosed
.: φ = 1/ϵ0 * q
Suppose a very long positive line charge having linear charge density λ. The field due to this charge will have cylindrical symmetry because all the points at a certain distance around the line charge are identical to view it. To find the electric field intensity E at a point P at a normal distance r from the conductor, let us draw a cylindrical Gaussian surface of length l and radius r so that point P lies at its curved surface as shown in the figure.
Here, the charge enclosed by the gaussian surface is q = λl
From Gauss theorem, electric flux passing through the closed surface is,
Φ= 1/ϵ0 * q
= 1/ϵ0 * λl …...... (i)
Also, the surface area of closed surface is
A = 2πrl …....... (ii)
So, the electric flux through the curved surface is
Φ = E. A = E. 2πrl
From equations (i) and (ii), we get
E. 2πrl = 1/ϵ0 * λl
.: E = λ/ 2πϵ0r …...... (iii)
Hence, the electric field intensity due to a long linear charge distribution depends only on the linear charge density but not on the total charge and length.
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