Question

Quadrupole charge distribution. Consider the four-charge distribution in the xy- plane along the x-axis, the y-axis, and in the x = y direction for positive charges at a (1,1), a (-1,-1) and negative charges at a (11) and a (-1,1). Take the absolute value of the charges to be the same and equal to q. a) Recall in class we found that for the dipole charge distribution there are two axes of symmetry defined to be straight lines to which the electric field is parallel and perpendicular to which the electric field is zero everywhere along the line. What are the axes of symmetry, defined in an identical manner for the four-charge distribution? b) Calculate the limiting behavior of the electric field for large distance from the origin along x and y axes.

Answer 1

Solution:

At point o (origin =): - E_net(at 0) = E Vector_1 + E Vector_2 + E Vector_3 + E vector_4 = 0 (pair of 2 cancels out each other) At point A: -(0,1)E_1 = kq/r^2(r = 1) for E_and E_2 E_3 = kQ/r^2(r = squareroot 5) for E_3 and E_4 same for point b(symmetrical) Hence we can say that k^cap axis or(z-axis) is the axis of symmetry where E^vector(net) = 0 E proportional 1/r^2 when r is large r rightarrow infinity E = 0 (as the z - axis)