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Electricity and Magnetism

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Zero Field Point Between Two Lines of Like Charge

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Figure 1 depicts two long, thin, parallel lines of charge, separated by a distance $l$. Line one is located at the origin of the $x$ axis and holds a charge per unit length of $\lambda_1$ C/m. Line two is located at the coordinate $x = l$ and holds a charge per unit length of $\lambda_2$ C/m.

Figure 1. “Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.”

Both $\lambda_1$ and $\lambda_2$ have the same sign of charge, and the relative magnitudes of the charge densities are:

$$\lambda_1 = 3\lambda_2$$

At what value of $x$ between line one and line two is the net electric field equal to zero? Answer in units of the distance $l$.