Question

2. In class we derived Eq 11.14 for the V and 11.16 for the A, due to an oscillating dipole. We started to determine the E in class but didn't finish. Start from the beginning and derive E, showing all steps a. b. Now find the B by following the steps below and showing all work i. What direction is A ? How do you know? ii. Rewrite the unit vector (currently in cartesian) for A in spherical coordinates ii. What are A, As As (The components of A)? iv. Now, find B. 3. Since you now have E and B find the power radiate / area (Poynting Vector). Show all work.

PLEASE DO NUMBER 3 NOT NUMBER 2

the attached doc is needed

Answer 1

Given data 3) This is not, however, the term that concerns us now. We are interested in the fields that survive at large distance from the source in the so - caused radiation - zone approximation 3 r > > c/w The wavelength r > > lambda On this region the potential reduces to V(r, theta, t) = P_ow/4 pi epsilon_0 c (cos theta/r) sin [(et - r/c)] \r\n The vector potential is determined by the current flowing in the wire. I(t) = d_2/dt z^= -qow sin (wt) z^A(r, t) = mu_0/4 pi integral^d/2_- d/2 = qow sin [w(t - r)]z^/r d2 Because the integration itself introduce a factor of d, we can to first order. Replace the integrated by its value at the centre. A(r, theta, t) = mu_0 P_0 w/4 pi r sin [w(t - r/c) z^consider the fim metal surface separated by a small distance and connected by a fine wire. The system is assumed to be as a whole electric natural.