Four electric charges are at the corners of a square of side a. Using a standard

Question

Four electric charges are at the corners of a square of side a. Using a standard Cartesian coordinate system the charge at point x = 0, y = 0 is +q. The remaining three charges at the other corners of the square are -q. Find the magnitude and direction of the electric field at the position of the charge -q, the coordinates of which are x = a, y = a. What is the electric force on this charge? A proton accelerates from rest in a uniform electric field of 640 N/C. At some time later, its speed is 1.20 Times 10^6 m/s (nonrelativistic since v is much less than the speed of light). The mass of a proton is 1.67 Times 10^-27 kg. Find the acceleration of the proton. How long does it take the proton to reach this velocity? A uniformly charged rod of length l is bent into the shape of a semicircle. If the rod has a total charge of-Q, find the magnitude and direction of the electric field at 0, the center of the semicircle. Which one of the diagrams below is not a possible electric field configuration for a region of space which does not contain any charges? Why?

Explanation / Answer

1) a) The electric field = kq/r^2

So, Ex (a,a) = kq[(-1/a^2) + (1/2a^2)*cos45] = -(kq/a^2)*0.646 (along –x-axis)

       Ey (a,a) = kq[(-1/a^2) + (1/2a^2)*sin45] = -(kq/a^2)*0.646 (along –y-axis)

      E = sqrt[Ex^2 + Ey^2] = 0.914*(kq/a^2)

      Direction = arctan(Ey/Ex) = 45 degree

b) Force = qE = 0.914*(kq^2/a^2) at 45 degree

4) option e) is correct.

    As electric field lines are straight always.

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