(There is a arrow symbol over the r in this problem denoting that it is a vector) Suppose there is a charge distribution p(r,t), which has spherical symmetry at anytime.In other words, p(r,t) only depends on the magnitude or r and t, but not on the angle of r. The velocity distribution of charges is spherically symmetrical, i.e v(r,t) is along the radial direction and only depends on the absolute value of r and t.
1) By using symmetry analysis, determine the distribution of B(r) (Both B and r have arrow symbols above them denoting they are vectors) Hint: you also need to know the fact that no magnetic monopoles exist.
2) What's the displacement current distribution Jd=(1/(4p))(dE/(dt)) (Note that there is an arrow above J and E in the previous equation noting that these are vectors and d is a subscript) Whats the relationship between Jd (the j has an arrow over it indicating it is a vector and d is a subscript) and the actual current density J (with an arrow over it indicating it is a vector J)? Explain why your result in part 1) is correct event though it looks counter intuitive.