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(A) The electric field due to an infinitely long line charge at a distance $r$ is given by $E = \frac{\lambda}{2\pi \epsilon_0 r}$.At the midpoint bet

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$\lambda / \pi \epsilon_0 R$

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(A) The electric field due to an infinitely long line charge at a distance $r$ is given by $E = \frac{\lambda}{2\pi \epsilon_0 r}$.At the midpoint between the two wires,the distance from each wire is $r = R$.The electric field due to the positively charged wire $(+\lambda)$ points away from it,and the electric field due to the negatively charged wire $(-\lambda)$ points towards it.Since the midpoint is between the wires,both electric field vectors point in the same direction (from the positive wire towards the negative wire).Therefore,the total electric field $E_{total} = E_1 + E_2 = \frac{\lambda}{2\pi \epsilon_0 R} + \frac{\lambda}{2\pi \epsilon_0 R} = \frac{2\lambda}{2\pi \epsilon_0 R} = \frac{\lambda}{\pi \epsilon_0 R}$.

Two infinitely long thin straight parallel wires are kept at a perpendicular distance of $2R$,having uniform linear charge densities $+\lambda$ and $-\lambda$ respectively. The magnitude of the electric field at the midpoint between the two wires will be . . . . . . .

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