A circular loop carrying current lies in the yz plane with its axis along the x-axis. a) Evaluate the line integral along the axis of the loop from to.∫∙=―1=+1

b) Show the result of the integral when. Note this result can be related to ∫∙→∞Ampere's law by closing the curve of integration with a semicircle of radius on which 1 for very large ≈01.

Ablock of mass m slides on a horizontal frictionless table with an initial speed v0 . it then compresses a spring of force constant k and is brought to rest. the acceleration of gravity is 9.8 m/s2. how much is the spring compressed x from its natural length? 1) x = v0*sqrt(k/(mg)) 2) x=v0*sqrt(m/k) 3) x=v0*((mk)/g) 4) x=v0*sqrt(k/m) 5) x=v0*(m/kg) 6) x=v0*sqrt((mg)/k) 7) x=(v0)^2/(2g) 8) x=v0*(k/(mg)) 9) x=(v0)^2/(2m) 10) x=v0*((mg)/k)