Problem 1. Electric field of an electric dipoleAn “electric dipole" is an arrangement of (typically) two charges that have equal magnitude and oppositesign. Suppose a charge -q is located on the z axis at z =-d/2 and a charge +q is located also on the z+d/2. Note that there is a factor of two in the positions relative to the example worked in theaxis at znotes for the symmetric charges. The reason for this difference will be explained in problem 2. Forsimplicity, we will calculate the field in the xsymmetry to generalize the result.z plane – i.e. for y = 0 – and then use the cylindrical%3Da. Calculate E(0, 0, 0).b. Calculate the complete electric field for x = 0. In other words obtain E(0, 0, z). You may expressyour results using absolute values in the denominator but then show the expressions with thecorrect signs in the regions z < -d/2, -d/2 < z < d/2, z > d/2.c. Calculate the complete electric field for z = 0. In other words obtain E(x, 0,0).d. Calculate the complete electric field for all z and x values, Ē(x, 0, z)e. Generalize your result from part d by making the replacement i → î1, x → r1 .

(a) The electric field at (0,0,0) is : E→q=-14πε0qd/22k^E→-q=-14πε0qd/22k^E=E→q+E→-q=-2πε0qd2k^

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