Two charged balls are placed in point A and B and the distance between them is 9,54cm. Each of the balls are charged with 8,0 x 10^-8 C. Find the scalar value and direction of the electric field in point C placed 5 cm from A and 6 cm from B.
Cosine Rule: a^2 = b^2 + c^2 - 2ab x cosθ
E = Ke x (q/r^2)
The Attempt at a Solution
I have calculated the electric field of A and B.
EA = 287680 N/C
EB = 199778 N/C
After that I used cosine rule to calculate EC and got EC = 255341 N/C. This is correct.
But when I try finding the direction I calculate the angle between EC and EA (β) like this:
β = cos^-1 ((EA^2 + EB^2-EC^2)/(2EAEB)) = 60 degrees
The solution says that I should calculate the angle between EC and EA (β), but that the equation looks like this:
β = cos^-1 ((EC^2 + EA^2-EB^2)/(2ECEA)) = 42,65 degrees
Why am I supposed to use that equation?