Question

Three charges each equal to ${10}^{-9}C$ are placed at the corners of equilateral triangle of side $1m$. The force on one of the charges is:

• A. $9\times {10}^{-9}N$
• B. $9\sqrt{3}\times {10}^{-9}N$
• C. $27\times {10}^{-9}N$
• D. $18\times {10}^{-9}N$

Answer 1

Answer: (B)

$9\sqrt{3}\times {10}^{-9}N$

Force on x direction cancel out each other.
Now force component in Y direction is:

$r=1m$

$k=9\times$${10}^9{Nm}^2/C^2$
$F_{net}=2\times \frac{k{q}^2}{(1m{)}^2}cos30$
$=2\times \frac{9\times {10}^9\times {10}^{-9}\times {10}^{-9}}{1}\times \frac{\sqrt{3}}{2}$
$F_{net}=9\sqrt{3}\times {10}^{-9}\hat{y}N$