Particles P1 and P2 are located in three dimensional space at the points (2.00,

Question

Particles P1 and P2 are located in three dimensional space at the points (2.00, 3.50, 1.75) mm and (3.50, 2.25, 2.00) mm. These particles carry charges of +3.00 C and +4.50 C respectively. What is the magnitude of the net force they exert on another particle P3, with charge 3.50 C, located at the origin? Particles P1 and P2 are located in three dimensional space at the points (2.00, 3.50, 1.75) mm and (3.50, 2.25, 2.00) mm. These particles carry charges of +3.00 C and +4.50 C respectively. What is the magnitude of the net force they exert on another particle P3, with charge 3.50 C, located at the origin?

Explanation / Answer

force due to P1 :

r = 2i - 3.5j + 1.75k mm

|r| = sqrt[2^2 + 3.5^2 + 1.75^2] = 4.39mm = 4.39 x 10^-3 m

F1 = k q1q2 r / |r|^3

= (9 x 10^9 x 3 x 10^-6 x 3.50 x 10^-6)(2i - 3.5j + 1.75k)x 10^-3 / (4.39 x 10^-3)^3

F1 = 2233.92i - 3909.36j + 1954.68k N

due to P2:
r = -3.50i + 2.25j -2k mm

|r| = sqrt[3.5^2 + 2.25^2 + 2^2] = 4.62mm = 4.62 x 10^-3 m

F2 = k q1q2 r / |r|^3

= (9 x 10^9 x 4.50 x 10^-6 x 3.50 x 10^-6)(-3.50i + 2.25j -2k)x 10^-3 / (4.62 x 10^-3)^3

F2 = -5031.13i + 3234.3j - 2874.93k N

Fnet = F1 + F2 = -2797.21i - 675.06j -920.25k N

magnitude of force = sqrt[ 2797.21^2 + 675.06^2 + 920.25^2]

      = 3021.08 N

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