Question

Net force on q1?

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Coulomb's Law: Example Net force on q1? q1 q2 q3 2.0 C d> 4.0 cm 0.04m 13 0 600 qi q3

Answer 1

Force on a charge q due to q' when separated by a distance r.

$\dpi{100} \vec{F} = \frac{1}{4\pi \epsilon_o}[\frac{qq'}{r^2}]\hat{r}$

So Force on q₁ due to q₃ is given by:

$\dpi{100} \vec{F}_{13} = -\frac{1}{4\pi \epsilon_o}[\frac{(2)(2)}{(0.04)^2}]\hat{x} = -2.25\times 10^{13}\hat{x}N$

And Force on q₁ due to q₂ is given by:

$\dpi{100} \vec{F}_{12} = -\frac{1}{4\pi \epsilon_o}[\frac{(2)(2)}{(0.04)^2}](cos60\degree \hat{x} + sin60\degree \hat{y}] = -1.125\times 10^{13}\hat{x}N - 1.95\times 10^{13}\hat{y}N$

So the net force on q₁ will be:

$\dpi{100} \vec{F}_{} = -(1.125 + 2.25)\times 10^{13}\hat{x}N - 1.95\times 10^{13}\hat{y}N$

$\dpi{100} \vec{F}_{} = -3.375 \times 10^{13}\hat{x}N - 1.95\times 10^{13}\hat{y}N$