A charge of -1.0 C is located at the origin, a second charge of 3.8 C is located

Question

A charge of -1.0 C is located at the origin, a second charge of 3.8 C is located at x = 0, y = 0.1 m, and a third charge of 11 C is located at x = 0.2 m, y = 0. Find the forces that act on each of the three charges.

q = -1.0 C ......... N + ........... N q = 3.8 C ........ N + ......... N q = 11 C ....... N +................. N
A charge of -1.0 C is located at the origin, a second charge of 3.8 C is located at x = 0, y = 0.1 m, and a third charge of 11 C is located at x = 0.2 m, y = 0. Find the forces that act on each of the three charges. q = -1.0 1/2 C ......... N j hat i hat +................. N j hat q = 11 C ....... N i hat + ......... N j hat q = 3.8 C ........ N i hat + ........... N

Explanation / Answer

1) for charge q = -1

k = 8.9874*10^9 Nm^2 / C^2

Fx = k*(1*10-6)*11*10-6/(0.2)^2 = 2.471 N , along +ve x axis

Fy = k*(1*10-6)*(3.8*10-6)/(0.1)^2 = 3.415 N ,along +ve y axis

2) for Charge q= 3.8

force between charge

3.8 and -1 will be along y axis which will be

Fy1 = k*(1*10-6)*3.8*10-6)/(0.1)^2 = 3.415 N , along -ve y axis

force between charge 3.8 and 11 will be

F = k*(3.8*10-6)*(11*10-6)/[(0.05)1/2]2 N or 7.513 N

this can be divided along x and y axis

Fx will be F* costheta or 7.513*2/(51/2) N or 6.72 N , along -ve a x axis

FY will be F*sintheta or 7.513*1/(51/2) N or 3.36 N , along +ve a y axis

so final answer would be

Fx = 6.72 N , along -ve a x axis

Fy = Fy1 - FY = 3.415-3.36 N or   0.055 N along -ve y axis

3) for charge q = 11

force between charge 11 and -1 will be along x axis which will be

Fx1 = k*(1*10-6)*11*10-6/(0.2)^2 = 2.471 N , along -ve x axis

force between charge 3.8 and 11 will be

F = k*(3.8*10-6)*(11*10-6)/[(0.05)1/2]2 N or 7.513 N

this can be divided along x and y axis

FX will be F* costheta or 7.513*2/(51/2) N or 6.72 N , along +ve a x axis

Fy will be F*sintheta or 7.513*1/(51/2) N or 3.36 N , along -ve a y axis

so final answer would be

Fx = FX - Fx1 = 6.72 - 2.47 N or 4.25 N along +ve x axis

Fy = 3.36 N along -ve y axis

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