Let's write the forces that act on charge q3 due to charges q1and q2:
F1=r2kq1q3,F2=r2kq2q3.
We can find the distance from the charges q1and q3 as well as q2 and q3 from the Pythagorean theorem:
r=(0.3 m)2+(0.4 m)2=0.5 m.Since, q1=q2 and r1=r2=r the magnitudes of two forces are equal. Let's write the components of forces F1 and F2 in projections on x and y axis:
F1cosθ+F2cosθ=2F1cosθ,−F1sinθ+F2sinθ=0.As we can see, y-components cancel out, so we can write the net force on q3:
Fnet=2r2kq1q3cosθ.We can find angle θ from the geometry:
θ=cos−1(0.5 m0.4 m)=36.86∘.Finally, we can find the net force on q3:
Fnet=2⋅(0.5 m)29⋅109 C2Nm2⋅(2⋅10−6 C)2cos36.86∘=0.23 N.Answer:
Fnet=0.23 N, in +x-direction.
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