Two positive charges of magnitude q are placed on the r-axis as shown. One is pl

Question

Two positive charges of magnitude q are placed on the r-axis as shown. One is placed at the origin and the other a distance d to the left of the first one. A third charge, with negative charge -q is placed a distance d up the y-axis. tq X aXIS (a) (6 points) Sketch the magnitude and direction of the electric field for points along the r-axis. You don't need to draw an infinite number of lines, just make sure you indicate what is happening for each of the three regions on the z-axis (x 0. Express your answer in terms of the electric force constant k, the charge q, the distance d, and (d) (8 points) Calculate the potential energy of this arrangment of charges. Express your answer in terms of the electric force constant k, the charge q, and the distance d.

Explanation / Answer

I will start with part b.

b) For x > 0 ( implies along+x axis)

the disatnce between any point "x" and -q = sqroot( d^2+ x^2) and angle = tan^ -1 ( d/x)

Ex = k ( q) / x^2 + k (q) / ( x+d)^2 + K ( -q) / ( d^2+x^2) cos [ tan^ -1 ( d/x) ]

Ey = K (-q) / ( d^2 +x^2) sin (  tan^ -1 ( d/x)

c) V = k ( q) / d + k(q) / ( d+x) + K(-a) / sqroot (x^2+ d^2)

d) Potential energy = K ( q^2) / d + K ( -q^2/ d sroot 2) + K ( -q^2/ d) = -kq^2/ d sroot (2)

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