The diagram below shows a dipole centered at the origin and along the x-axis. De
ID: 1561890 • Letter: T
Question
The diagram below shows a dipole centered at the origin and along the x-axis. Determine an expression for the total electric field at a point A (r = 3.7L, 0) in terms of q and L. Calculate the magnitude of the total electric field at A, when q = 6.45times 10^-7 C| and L = 43.8 cm|. Consider the situation as described in the diagram. For each of the following statements, determine whether it is true or false. The direction of the net electric field at a point on the negative y-axis is SE The direction of the net electric field at a point on the positive y-axis is W The direction of the net electric field at A is W The direction of the net electric field at the point (-r, 0) is E The direction of the net electric field at the origin is W The magnitude of the net electric field at point A is greater than the magnitude of the net electric field at the origin.Explanation / Answer
Given :-
L = 0.438 m
r = 3.7L = 3.7 x 0.438 = 1.621 m
q = 6.45 x 10^-7 C
we can calculate the electric field at each end of the dipole and then vector add the fields together. The electric field experienced by a point charge is
E = F/q = kq / r^2
The field from the negative charge is
E1 = -kq / (L + r)^2
The field from the positive charge is
E2 = kq / (r - L)^2
E1 + E2 = kq / (r - L)^2 - kq / (L + r)^2
E1 + E2 = kq[1 / (r - L)^2 - 1 / (L + r)^2]
= (9 x 10^9 x 6.45 x 10^-7)[1 / (1.621 - 0.438)^2 - 1 / (0.438 + 1.621)]
= 2250 N/C