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Question

Find the electric field vector at P(a,a,a) due to three infinitely long lines of charges along the x, y and z axis, respectively. The charge density i.e. charge per unit length of each wire is λ.



A
λ3πε0a(ˆi+ˆj+ˆk)
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B
λ2πε0a(ˆi+ˆj+ˆk)
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C
λ22πε0a(ˆi+ˆj+ˆk)
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D
2λπε0a(ˆi+ˆj+ˆk)
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Solution

The correct option is B λ2πε0a(ˆi+ˆj+ˆk)
Let us consider electric field due to wire 3 only.


E3=Eˆr=λ2πε0(a2+a2)12(ˆicos 450+ˆjcos 450)=λ22πε0a12(ˆi+ˆj)=λ4πε0a(ˆi+ˆj)Similarly, electric field due to wires (1) and (2) E1=λ4πε0a(ˆj+ˆk) and E2=λ4πε0a(ˆi+ˆk)Enet=E1+E2+E3 =λ2πε0a(ˆi+ˆj+ˆk)

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