Consider two point charges held in close proximity to one another; q_1 = e at (0
ID: 1716551 • Letter: C
Question
Consider two point charges held in close proximity to one another; q_1 = e at (0, d/2,0), and an opposite charge q_2 = -e at (0, -d/2,0) where d = 1 Times 10^-10 in (1 angstrom) Mow much energy U (x, y, z) is required to bring a third "test charge" q_3 in from infinity to an arbitrary point (x, y, z) m? What is the force P(0,y, 0) on q3 at (0, y, 0) if y = 1 mu m and q3= e? What is the electric field E(0,y,0) at an arbitrary point on the x axis (0, y, 0) due to q_1 and q_2? Use the binomial expansion to show that far away from q_1 and q_2, the field E(0, y, 0) ~ p/2 pi epsilon_0 y^3 j asymptotically decreases as one over the distance cubed, where p is the dipole moment.Explanation / Answer
The component of the field at (0,1,0) can be
E(0,1,0)=(q/4)d/(1/4d2+y2)3/2
(e/4)1*10-10/(1/4*10-10+1)3/2=e
V(x)=kq[2/(x2+a2)1/2+1/x-a]
Ex(x)=-dv/dx[kq(2/(x2+a2)1/2+1/a-x=p/2cosy3