A very long uniform line of charge has charge per unit length λ1 = 4.68 μC/m and lies along the x-axis. A second long uniform line of charge has charge per unit length λ2 = -2.48 μC/m and is parallel to the x-axis at y1 = 0.400 mWhat is the magnitude of the net electric field at point y2 = 0.200 m on the y-axis?

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aristocles aristocles · Answer 1 · 2019-11-10T07:11:54+01:00

Answer:

[tex]E_{net} = 6.44 \times 10^5 N/C[/tex]

Explanation:

As we know that electric field due to infinite line charge distribution at some distance from it is given as

[tex]E = \frac{2k \lambda}{r}[/tex]

now we need to find the electric field at mid point of two wires

So here we need to add the field due to two wires as they are oppositely charged

Now we will have

[tex]E_{net} = \frac{2k\lambda_1}{r} + \frac{2k\lambda_2}{r}[/tex]

now plug in all data

[tex]\lambda_1 = 4.68 \muC/m[/tex]

[tex]\lambda_2 = 2.48 \mu C/m[/tex]

[tex]r = 0.200 m[/tex]

now we have

[tex]E_{net} = \frac{2k}{r}(4.68 + 2.48)[/tex]

[tex]E_{net} = \frac{2(9\times 10^9)}{0.200}(7.16 \times 10^{-6})[/tex]

[tex]E_{net} = 6.44 \times 10^5 N/C[/tex]