Key to "Three charges are arranged as shown in Figure...."

necessaryh

Answered question

2021-03-23

Three charges are arranged as shown in Figure. Find the magnitude and direction of the electrostatic force on the charge at the origin.

Mayme

Skilled2021-03-25Added 103 answers

Force between two charges on x-axis is repulsion force, so the force on charge at origin acts in negative x-direction

F_{1} = k (6 \cdot 10^{- 9}) \frac{5 \cdot 10^{- 9}}{{(0.03)}^{2}} = 8.98 \cdot 10^{9} \cdot (6 \cdot 10^{- 9}) \frac{5 \cdot 10^{- 9}}{{(0.03)}^{2}}

= 2993.33 \cdot 10^{- 9}

N
Force between two charges on y-axis is attractive force, so the force on charge at origin acts in negative y-direction

F_{2} = k (3 \cdot 10^{- 9}) \frac{5 \cdot 10^{- 9}}{{(0.01)}^{2}} = 8.98 \cdot 10^{9} \cdot (3 \cdot 10^{- 9}) \frac{5 \cdot 10^{- 9}}{{(0.01)}^{2}}

angle made by the net force with positive x-axis = 180 + taninverse

\frac{13470 \cdot 10^{- 9}}{2993.33 \cdot 10^{- 9}} = 180 + 77.47 = 257.77

degrees
magnitude of force

= \sqrt{13470^{2} + {2993.33}^{2}} \cdot 10^{- 9} = 13798.5 \cdot 10^{- 9}

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