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Electric Charges and Fields
Electric Field due to an Infinite Line Charge
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- field between two opposite line charges
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2019 1 question
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Two parallel infinite line charges with linear charge densities $+\lambda\ C/m$ and $-\lambda\ C/m$ are placed at a distance of $2R$ in free space. What is the electric field mid-way between the two line charges?[add image: two parallel line charges +λ and −λ separated by 2R, fields E1 and E2 at the midpoint] Field due to each line charge at distance $R$: $E=\frac{\lambda}{2\pi\epsilon_0R}$ At the midpoint both fields point in the same direction (from $+\lambda$ towards $-\lambda$): $\vec{E}_1=\frac{\lambda}{2\pi\epsilon_0R}\hat{i}$, $\vec{E}_2=\frac{\lambda}{2\pi\epsilon_0R}\hat{i}$ $\vec{E}_{net}=\vec{E}_1+\vec{E}_2=\frac{\lambda}{\pi\epsilon_0R}\hat{i}\ N/C$
