Three charges, each of magnitude 8 nC, are at separate corners of a square of ed

Question

Three charges, each of magnitude 8 nC, are at separate corners of a square of edge length 8 cm. the two charges at opposite corners are positive, and the other charge is negative. Find the force exerted by these charges on a fourth charge q = + 3 nC at the remaining (upper right) corner. (Assume the + x axis is directed to the right and the + y axis is directed upward.) You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question.

Explanation / Answer

Force of top left charge on q = [9.00 x 109 * 8.0 x 10-9 * 3.0 x 10-9] / [0.08²]

Ftl = F1 = 3.375 x 10-5i N

Force is horizontally to the right from q

Force of bottom right charge on q has the same magnitude as F1 but is directed vertically up the page from q

so Fbr = F2 = 3.375 x 10-5j N

The charge at the bottom left corner is [0.08² + 0.08²] = 0.11313 m from q

so the magnitude of the force of the bottom left charge on q:

Fbl = [9.00 x 109 * 8.0 x 10-9 * 3.0 x 10-9] / [0.11313]
Fbl = 1.9091 x 10-6 N

its direction counterclockwise from the +x-axis = 180° + arctan (0.08 / 0.08) = 180° + 45° = 225° [the two charges are opposite sign so will attract each other]

so i component for F3 = 1.9091 x 10-6 cos 225°

and the j component for F3 = 1.9091 x 10-6 sin 225°

F3 = 1.9091 x 10-6 cos 225°i + 1.9091 x 10-6 sin 225°j
F3 = -1.35 x 10-6 i - 1.35 x 10-6 j

The resultant force on q = F1 + F2 + F3

R = 3.24 x 10-5 i + 3.24 x 10-5 j N

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