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
λ2√2πε0a(ˆi+ˆj+ˆk)
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D
√2λπε0a(ˆi+ˆj+ˆk)
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Solution
The correct option is Bλ2πε0a(ˆi+ˆj+ˆk) Let us consider electric field due to wire 3 only.
−⇀E3=Eˆr=λ2πε0(a2+a2)12(ˆicos450+ˆjcos450)=λ2√2πε0a1√2(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)