In this problem, you are to show that the generalized form of Ampres law (Equation 32-4) and

In this problem, you are to show that the generalized form of Ampère’s law (Equation 32-4) and the Biot– Savart law give the same result in a situation in which they both can be used. Figure shows two charges +Q and –Q on the x axis at x = –a and x = +a, with a current I = – dQ/dt along the line between them. Point P is on the y axis at y = R.

 (a) Use the Biot–Savart law to show that the magnitude of B at point P is

(b) Consider a circular strip of radius r and width dr in the yz plane with its center at the origin. Show that the flux of the electric field through this strip is

(c) Use your result for part (b) to find the total flux fe through a circular area of radius R. Show that

(d) Find the displacement current Id, and show that

 (e) Then show that Equation 32–4 gives the same result for B as that found in part (a).

Transcribed Image Text:

dø. f, B.dl = Ho(1 + I4) = Hol+ HE0 32-4 %3D dt +Q