(There is a arrow symbol over the r in this problem denoting thatit is a vector) Suppose there is a charge distribution p(r,t),which has spherical symmetry at anytime.In other words, p(r,t) onlydepends on the magnitude or r and t, but not on the angle of r. Thevelocity distribution of charges is spherically symmetrical, i.ev(r,t) is along the radial direction and only depends on theabsolute 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 arevectors) Hint: you also need to know the fact that no magneticmonopoles exist.
2) What's the displacement current distributionJd=(1/(4p))(dE/(dt)) (Note that there is an arrow above J and E inthe previous equation noting that these are vectors and d is asubscript) Whats the relationship between Jd (the j has an arrowover it indicating it is a vector and d is a subscript) and theactual current density J (with an arrow over it indicating it is avector J)? Explain why your result in part 1) is correct eventthough it looks counter intuitive.
(There is a arrow symbol over the r in this problem denoting thatit is a vector) Suppose there is a charge distribution p(r,t),which has spherical symmetry at anytime.In other words, p(r,t) onlydepends on the magnitude or r and t, but not on the angle of r. Thevelocity distribution of charges is spherically symmetrical, i.ev(r,t) is along the radial direction and only depends on theabsolute 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 arevectors) Hint: you also need to know the fact that no magneticmonopoles exist.
2) What's the displacement current distributionJd=(1/(4p))(dE/(dt)) (Note that there is an arrow above J and E inthe previous equation noting that these are vectors and d is asubscript) Whats the relationship between Jd (the j has an arrowover it indicating it is a vector and d is a subscript) and theactual current density J (with an arrow over it indicating it is avector J)? Explain why your result in part 1) is correct eventthough it looks counter intuitive.
