Question

3. Starting with Ampere's law, find the magnetic field at r from the axis, inside and outside of a circular toroid, figure below, of major radius R and minor radius a, wrapped with N turns of wire carrying current I. Evaluate for r=R=5cm, a=2cm,N=1000,1=3A

Answer 1

Finding the magnetic field inside or outside a toroid is a good example of the power of Ampere's law. we should note here that by given data the region between r greater (R-a) and smaller than (R+a) is the region inside the toroid. While region with r greater than R+a and smaller than (R-a) is the region outside the toroid.

Let us see both the cases one by one-

Fram Ampere's cirauital law- we know, 6.di ,Cnet afeche areut J Total auareut rougl amperial loop Total tunn XI h: turni per Bdicose NT (Bis. coustaut). B Magnetude of ue Nagnelic freld 8.9KR NI turn per uust leugt |B - Upu h true of Magnelie freld iuside a toroid Thi's From, qiren value, ARXI0 u/m 8: 0NI arR 1257 x 1o 12.57 XID X 1000 X 3 2N x 0.05 Au

For Region outside the toroid,

Now, lets pd out a magneic e outside toroid r CR-a) .e, when we take we need to apply Ampere's laus we cuooce ocu pau to be a loced cir cular loop Wat te outsfde toroid The tadiuu of u cuau pal fc given by r. Cr A Ra) we could haue choseu CrA R-a) au wel Result would be same aunpere oup Oatside He toroid what is e net oureut at s eudlosed b It eucloses N 0ops of wre leat direciau Cupuard) aud N oep at Oppocite direciou (dowupards Teucosed 0 pauay u one cuarend I camy Hence 0 This would be same foo CrzRas B O Fos auy given valu af R aud N 13 wowd alway be 2aro AM 96

Thank you.