An infinitely long uniform line charge distribution of charge per unit length lies parallel to the y-axis in the y-z plane at (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is ( =permittivity of free space), then the value of n is
Imagine , a cylindrical gaussian surface of length L and radius a.
Given rectangular surface ABCD subscribes an angle at the infinity long uniform line of charge.
The total angle subscribe by cylinder is and charge enclosed is .
Flux through the rectangle is same as the flux through of the hexagon since it subtends at P and field lines are symmetrically radially outwards.
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Two nonconducting plates A and B of radii 2R and 4R, respectively, are kept at distances x and 2x from the point charge q. A surface cutout of a nonconducting shell C is kept such that its center coincides with the point charge. Each plate and spherical surface carries surface charge density .
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