2019 Electric Charges and FieldsElectric Field due to an Infinite Line Charge Medium Question 16 of 42 in Electric Charges and Fields

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?

A zero
B $\frac{2\lambda}{\pi\epsilon_0R}\ N/C$
C $\frac{\lambda}{\pi\epsilon_0R}\ N/C$
D $\frac{\lambda}{2\pi\epsilon_0R}\ N/C$

The answer is C.

Solution

[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 $-\lambda$): $\vec{E}_1=\frac{\lambda}{2\pi\epsilon_0R}\hat{i}$, $\vec{E}_2=\frac{\lambda}{2\pi\epsilon_0R}\hat{i}$ $\vec{E}_{net}=\vec{E}_1+\vec{E}_2=\frac{\lambda}{\pi\epsilon_0R}\hat{i}\ N/C$

Concept field between two opposite line charges

Electric Charges and Fields in past papers

42 questions from this chapter have appeared across 23 exam years.