(a) Let\'s draw circular Ampere\'s loops symmetrically placed within (enclosing)

Question

(a) Let's draw circular Ampere's loops symmetrically placed within (enclosing) a circular current loop as shown in the figure. Make an argument on why Ampere's law is not much of a help in getting the magnetic field magnitude using these loops despite the fact the field is, from the symmetry, is constant along these Ampere's loops.

A top angle view of circular current. The dashed circles Ampere's loop examples. A cross section of an ideal solenoid. The dashed rectangle are Ampere's loop examples.

Explanation / Answer

a) since the circle is radially symmetric the magnetic field will have the same magnitude
along the circle put will point different directions

so when we integrate everything up around the circle we will get 0

i.e. integral of B dl = 0

so we can't find B since it dissapeared

b)since B is constant in the solenoid, when we integrate around the loop the top and bottom will cancel

so integral of B dl = 0 so no way to solve for B

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