Forces in a Three-Charge System Coulomb\'s law for the magnitude of the force F

Question

Forces in a Three-Charge System Coulomb's law for the magnitude of the force F between two particles with charges Q and Q' separated by a distance d is QQ where K s and 4TE Eo 8.854 x 10 12 C2/(N m2) is the permittivity of free space Consider two point charges located on the X axis: one charge, q 15.5 nC is located at al z1 1.670 m the second charge g2 39.0 nC, is at the origin (z 0.0000) Part A What is the net force exerted by these two charges on a third charge q3 45.5 nC placed between q1 and Q2 at T3 1.240 m Your answer may be positive or negative, depending on the direction of the force. Express your answer numerically in newtons to three significant figures. Force on q3 Submit Hints My Answers Give Up Review Part

Explanation / Answer

Given that :

charge on q1 = -15.5 x 10-9 C

charge on q2 = 39 x 10-9 C

charge on q3 = 45.5 x 10-9 C

distance at x1 = -1.67 m

distance at x3 = -1.24 m

the net force exerted by these two charges on a third charge which will be given as :

Fnet = F13 + F23

Fnet = k q1 q3 / x132 + k q2 q3 / r232

where, k = 9 x 109 Nm2/C2

inserting the values in above eq.

Fnet = [(9 x 109 Nm2/C2) (-15.5 x 10-9 C) (45.5 x 10-9 C) / (1.67 m - 1.24 m)2] - [(9 x 109 Nm2/C2) (39 x 10-9 C) (45.5 x 10-9 C) / (1.24 m)2

Fnet = [-(6347.2 x 10-9 Nm2) / (0.1849 m2)] - [(15970.5 x 10-9 Nm2) / (1.5376 m2)]

Fnet = (-34327.7 x 10-9 N) - (10386.6 x 10-9 N)

Fnet = -44714.3 x 10-9 N

Fnet = -4.47 x 10-5 N

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