Consider a group of charged toner particles and how one of them can be moved aro

Question

Consider a group of charged toner particles and how one of them can be moved around in the group. Four charged particles form a square with side length a = 6.9 mum. Particles 1, 3, and 4 carry charge +q - 3.9 Times 10^-15 C, and particle 2 carries charge -2q. Particles 2 and 4 are diagonally opposite each other. How much work must be done by an external agent on particle 4 to pull it out of its corner, slide it around outside the perimeter of the square past particles 3, 2, and 1, and then place it stationary at the center of the square?

Explanation / Answer

The electric field is a conservative field so it doesn't matter by which path we take the particle to its new position, we might as well shift it directly.

distance from the corners to the centre = 1.414*6.9/2 = 4.8 mirco m

Work done = q*(V1-V2) = q*(V1+V2+V3) = 3.9*10-15*(3.9*10-15/6.9*10-6 - 2*3.9*10-15/9.6*10-6 + 3.9*10-15/6.9*10-6) - 3.9*10-15*(3.9*10-15/4.8*10-6 - 2*3.9*10-15/4.8*10-6 + 3.9*10-15/4.8*10-6)

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