The figure shows the net force experienced by a positive test charge located at

Question

The figure shows the net force experienced by a positive test charge located at the center of the diagram. The force comes from two nearby charged balls, one (in red) with a charge of +Q and one (in green) with an unknown charge. (a) Choose the two correct statements, from the list below, about the sign and magnitude of the charge on the second ball. (As with all multiple select questions, you must select all of the correct answers, and only the correct answers, to receive credit for the question.) The second ball has a positive charge. The second ball has a negative charge. There is not enough information here to determine the sign of the charge on the second ball. The magnitude of the charge on the second ball is greater than Q. The magnitude of the charge on the second ball is less than Q. The magnitude of the charge on the second ball is equal to Q. (b) If Q = 5.80 microcoulombs, determine the charge (sign and magnitude) on the second ball. microcoulombs

Explanation / Answer

considering upward direction as +ve y axis and to the right as +x axis
and i and j to be unit vectorsd along x and y axis
let chargfe on the other ball be q

so, Force on test particle of charge q'
F = kq' [ -Qj/4x^2 - qi/4x^2], where x is the side of one box
so, angle with x axis, arctan(Q/q) = -1/2
tan(-1/2) = Q/q
q = -114.588Q

a. The second ball has -ve charge
   the magnitude of charge on the second ball is greater than the magnitude of charge on the first ball
b. Q = 5.8*10^-6 C
   then q = -114.588Q = -664.614*10^-6 C = -664.614 micro C

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