- #1
Jahnavi
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Homework Statement
Homework Equations
The Attempt at a Solution
In the region |z|<1 ,
E(z) = -dV/dz = 10zk
This means there is a variable electric field in the region -1<z<1 .In the +z region it is directed in the +z direction and vica versa .
For finding the charge density in the region 0<z<1, I need to apply Gauss's law . I am not supposed to use differential form of Gauss law .
Consider at a distance z from the origin a thin cuboid of side a×a and height ∆z .
The two square faces are at distances z1 and z2 , z2>z1
Flux through the closed cuboidal box would have a contribution from only these two square surfaces which are perpendicular to the electric field .
Net flux = E(at z2)a2 - E(at z1)a2 = 10a2z2-10a2z1
Applying Gauss law ∫E⋅ds= ρa2∆z/ε
10a2z2-10a2z1 = ρa2∆z/ε
10a2∆z = ρa2∆z/ε
ρ = 10ε in the region 0<z<1
Is that right ?
Please help me with this problem .
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