Answer Happy

Question 13 (F): Consider the same parallel plate capacitor as in the previous problem, with the same current flowing onto the left-hand plate and off the right-hand plate. This question explores another (meaning not starting from charge conservation) motivation for fixing Ampere's Law. There is an Amperian loop (shown, Figure 6, right). Consider our static version of Ampere's Law: Х 7 x B = Moſ Stoke's Theorem tells us that if this is true, then for any surface bound by the Amperian loop, B. di = Molenclosed where lenclosed = . nda where the surface integral at right is carried out over the (any) surface bounded by the contour used for the path integral at left. a) Consider the surface Si bounded by the Amperian loop (Figure 6, right). What is lenclosed on that surface? b) Consider the surface S2, also bounded by the Amperian loop (Figure 6, right). What is lenclosed on that surface? c) Since the surface integrals over S, and S2 are not the same, then we know there is a fundamental problem with the static version of Ampere's Law. In this case i=dq/dt, can you come up with a quantity related to dq/dt that, integrated over the surface S2 gives i? If you cannot, do not worry about it... we really should not be able to make Nobel-Prize-worthy leaps of intuition as part of answering one question in a third-year course!