Question

1. From Quiz: Noting that ▽ ×B=Pol + μ。Eoat and ▽ × Λ-Band E-w-a-show that 2. In class we derived Eq 11.14 for the Vand 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. ili. What are A As Ap(The components of A)? iv. Now, find B.

Please Do # 1
Thanks

Answer 1

Given Maxwell equation nabla^- times B^- = mu_0 J^- + mu_0 t_0 partial differential E^-/partial differential t And nabla^- times A^= B^- - (1), E^- = -nabla V - partial differential A^-/partial differential t - (II) So we can Modify the above Maxwell eq^n nabla^- times B^- = mu_0 J^- + mu_0 E_0 partial differential E^-/partial differential t = > nabla^- times (nabla^- times A^-) = mu_0 J^- + mu_0 t_0 partial differential/partial differential t (-nabla V - partial differential A^-/partial differential t) (eq^n (1) & eq^n (II) used) = > nabla (nabla^-.A^-) - nabla^2 A = mu_0 J^- + mu_0 t_0 [partial differential/partial differential t (-nabla V) - partial differential^2 A^-/partial differential t^2] = > nabla^2 A - nabla^- (nabla^-.A^-) + mu_0 J^- - mu_0 t_0 nabla (partial differential V/partial differential t) - mu_0 t_0 partial differential^2 A^-/partial differential t^2 = 0 = > [nabla^2 A - mu_0 t_0 partial differential^2 A^-/partial differential t^2] - nabla [(nabla^-.A^-) + mu_0 t_0 partial differential V/partial differential t] + mu_0 J = 0 = > [nabla^2 A - mu_0 t_0]