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A positive point charge q1 creates an electric field of magnitude e1 at a spot located at a distance r1 from the charge. the charge is replaced by another positive point charge q2, which creates a field of magnitude e2 = e1 at a distance of r2 = 2r1. how is q2 related to q1?

Respuesta :

Hummingbeard
Let's answer this in a straightforward way:
The Electric field due to a point charge at a point with distance r relative to the point charge is:
[tex]E(r)=\frac{1}{4\pi\epsilon_0}\frac{q}{r^2}[/tex]
For E1 we have is:
[tex]E_1=\frac{1}{4\pi\epsilon_0}\frac{q_1}{r^2_1}[/tex]
For E2=E1 we have:
[tex]E_2=\frac{1}{4\pi\epsilon_0}\frac{q_2}{r^2_2}[/tex]

We the get the following equation:
[tex]E_1=E_2\implies \frac{q_1}{r^2_1}=\frac{q_2}{r^2_2}\implies q_2=q_1\frac{r^2_2}{r^2_1}[/tex]

Because [tex]r_2=2r_1[/tex] we get from the above expression for q2:
[tex]q_2=q_1\frac{r^2_2}{r^2_1}=q_1\frac{(2r_1)^2}{r^2_1}=q_1\frac{4r^2_1}{r^2_1}=4q_1[/tex]