Consider three charges arranged in a triangle as shown. + - + 0.266 m 0.599 m −3.4 nC 8.1 nC 4.8 nC y x What is the net electric force on the charge at the origin? The value of the Coulomb constant is 8.99 × 109 N · m2 /C 2 . Answer in units of N. 010 (part 2 of 4) 10.0 points What is the direction of this force (as an angle between −180◦ and +180◦ measured from the positive x-axis, with counterclockwise positive)? Answer in units of my work: 3.49913223E-6/9.74164509E-7=3.591931545

Question

tan^-1(3.59193545)=74.44 degrees (wrong?)

Answer 1

The magnitudes of the forces exerted on the charge at the origin can be calculated like this:
F12 = k*|q1*q2|/r12^2
F13 = k*|q1*q3|/r13^2
where k is the Coulomb constant (8.99 × 10^9 N·m^2/C^2), q1 is the charge at the origin (-3.4 nC), q2 and q3 are the other charges (8.1 nC and 4.8 nC), and r12 and r13 are the distances between charges, respectively.

F12 = (8.99 × 10^9 N·m^2/C^2) * |(-3.4 × 10^(-9) C) * (8.1 × 10^(-9) C)| / (0.266 m)^2
F12 ≈ 3.20 × 10^(-8) N

F13 = (8.99 × 10^9 N·m^2/C^2) * |(-3.4 × 10^(-9) C) * (4.8 × 10^(-9) C)| / (0.599 m)^2
F13 ≈ 2.15 × 10^(-9) N

Now, we need to find the components of those forces in the x and y direction. Let's denote the angle between F12 and the x-axis as theta_12, and the angle between F13 and the x-axis as theta_13. From the geometry, we have:
theta_12 = atan(0.599 / 0.266)
theta_13 = 0

Therefore, the x and y components of the forces are:

F12x = F12 * cos(theta_12)
F12y = F12 * sin(theta_12)
F13x = F13 * cos(theta_13)
F13y = F13 * sin(theta_13)

Calculating those:

F12x ≈ 2.549 × 10^(-8) N
F12y ≈ 7.137 × 10^(-9) N
F13x ≈ 2.15 × 10^(-9) N
F13y = 0 N

The net force components can be calculated by adding the components of the two forces:

Fnet_x = F12x - F13x ≈ 2.33 × 10^(-8) N
Fnet_y = F12y = 7.137 × 10^(-9) N

Now we can find the magnitude and direction of the net force:

Fnet = sqrt(Fnet_x^2 + Fnet_y^2) ≈ 2.50 × 10^(-8) N

theta_net = atan(Fnet_y / Fnet_x)= atan(7.137 × 10^(-9) N / 2.33 × 10^(-8) N) = 16.98°

So the magnitude of the net electric force on the charge at the origin is about 2.50 × 10^(-8) N, and its direction is 16.98° counterclockwise from the positive x-axis.