Consider two current loops of radius = 4 cm (both), that share the same axis, bu

Question

Consider two current loops of radius = 4 cm (both), that share the same axis, but are separated by 10 cm. Loop one carries a current 4 amperes, while loop 2 carries a current 8 amperes but in the opposite direction. 10 cm -4 A a) Write the expression for the magnetic field on the axis between the two coils at an arbitrary point P. Modify the expression we derived in class so that z of point P is measured from the midpoint O as shown. As a hint in this problem, start by figuring out the DIRECTION of the magnetic field due to each current loop, then write down the expression for its magnitude. Bonus (difficult) Using part a), find the point on the axis where the magnetic field vanishes identically.

Explanation / Answer

Biot Savart's law says

mganetic field Bz = (mue0 I/2)(r^2/(z^2+r^2)^3/2)    r radius, z is perpencicular distance from the circular loop

due to upper circular loop the magnetic field is into the page and due to lower one is out of the page

given radius r = 4 cm = 0.04 m, current upper loop is 8 A , lower one of 4 A

   point O is 5 cm from each loop

   so magnetic field is
       Bz = (mue0 I/2)(r^2/(z^2+r^2)^3/2)

           = (4*pi*10^-7*8/2)(0.04^2/(0.05^2+0.04^2)^(3/2))
      

            = 3.0634*10^-5 T
due ot lower loop

       Bz = (mue0 I/2)(r^2/(z^2+r^2)^3/2)

           = (4*pi*10^-7*4/2)(0.04^2/(0.05^2+0.04^2)^(3/2))
  

           = 1.5317*10^-5 T

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---