1. The problem statement, all variables and given/known data Consider the following figure. For the electric dipole shown in the figure, express the magnitude of the resulting electric field as a function of the perpendicular distance x from the center of the dipole axis. (Use the following as necessary: k, q for the charges, x, and d.) 2. Relevant equations E_{t}= E_{1} + E_{2} E = k|q|/r^{2} 3. The attempt at a solution The x component of the electric fields will cancel out, leaving only the y-components. Adding the two vector fields in the y-direction: [k|q|/r^{2}]sinθ + [k|q|/r^{2}]sinθ = 2[k|q|/r^{2}]sinθ r^2 = [d/2 + x^2]^{1/2} My final answer: 2[kq/[d^{2}/4 + x^{2}]^{1/2}]sinθ This is not correct.
For one thing r^2=x^2+(d/2)^2. You've got an extra square root. For another, you should be able to express sinθ in terms of x and d as well.
Yes, I noticed that extra square root. When I fix things up, and set sinθ equal to d/2r: It's a lot of algebra, but it comes out to kqd/[(d^{2}/4)+x^{2})]^{3/2}. Does that look right?
All right. Thanks. Webassign doesn't like the answer but I feel confident in the math. Could be a problem with Webassign.