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Question

The electrostatic potential due to certain charge distribution is given by V (x, y, z) = - Voa4 (x + y + z) xyz. In Column I, the values of electric field (in terms of Voa) and charge density (in terms of Voεoa2 are given. In Column II, different points in space are given. Each value in Column I may correspond to one or more quantities in Column II.

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Solution

We know that,
E=ϕ
.E=ρ/ϵ0
Therefore,
ϕ=V0/a4×xyz(x+y+z)
E=V0/a4×((2xyz+y2z+z2y)^i+(2xyz+x2z+z2x)^j+(2xyz+x2y+xy2)^k)
ρ=ϵ0×V0/a4×(2yz+2xz+2xy)
Now,
ρ(a,a,a)=ϵ0×V0/a4×6a2=6ϵ0V0/a2
E(0,0,a)=V0/a4×(0)=0
ρ(0,a,a)=ϵ0×V0/a4×2a2=2ϵ0V0/a2
E(a,a,a)=V0/a4×4a3^i+4a3^j+4a3^k
E(0,a,a)=V0/a4×2a3^i

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