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Problem 1 (38 points):
Particle 1 of charge $q_1 = 3.48 \times 10^{-4}$ C, particle
2 of charge $q_2 = 6.30 \times 10^{-4}$ C, and particle 3 of
charge $q_3 = -1.01 \times 10^{-4}$ C are placed at the
vertices of a rectangular triangle. The hypotenuse
of the triangle is 5.00 m long, and the legs of the
triangle are 3.00 m long along the x-axis and 4.00
m long along the y-axis as shown in the figure.
Subsequently, the angles of the triangle are 53.1°
and 36.9° as shown in the figure as well. Our goal
is to find the resultant electrostatic force on
particle 3, $\overrightarrow{F_3} = \overrightarrow{F_{13}} + \overrightarrow{F_{23}}$.
a) What are the directions of the force vectors $\overrightarrow{F_{13}}$
and $\overrightarrow{F_{23}}$ that particle 1 and particle 2 respectively exert on particle 3? Draw and
label both the force vectors on the figure, answers like "left", "right", "away", "toward",
etc. won't be accepted.
b) What is the magnitude $F_{13}$ of force $\overrightarrow{F_{13}}$ that particle 1 exerts on particle 3 ?
c) What is the magnitude $F_{23}$ of force $\overrightarrow{F_{23}}$ that particle 2 exerts on particle 3 ?
d) For the coordinate system, chosen in the figure, calculate the x- and y- components
of the resultant electrostatic force $\overrightarrow{F_3} = \overrightarrow{F_{13}} + \overrightarrow{F_{23}}$ on particle 3.
e) Calculate the magnitude of the resultant electrostatic force $\overrightarrow{F_3} = \overrightarrow{F_{13}} + \overrightarrow{F_{23}}$ on
particle 3.
f) Find the direction of the resultant electrostatic force $\overrightarrow{F_3} = \overrightarrow{F_{13}} + \overrightarrow{F_{23}}$ on particle 3.
Express your answer in terms of a counterclockwise angle with the positive x-axis.
(Answers like "upright" or "downright" won't be accepted.)
Present all your answers within the precision of 3 significant figures.
Start here and use the next page to continue showing your work and final answers.
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