Question

3. This question concerns the Biot-Savart law. (a) Give the meaning of each term in the equation and describe how the equation is used to calculate a magnetic field strength. (b) Consider a rectangular loop of wire; the long side is length a and the short side length b. Referring to the derivation of the field for an infinite wire obtain the field strength B for a single wire of finite length at a distance L from the centre of the wire. (c) If a current I flows in the loop and a >b, what is the magnetic field strength in the plane of the wire, at a distance d from the centre of the long wire in the plane of the loop and in the limit d »a? (d) What is the magnetic field at the centre of a square loop of wire, with sides of length a and current I?

Answer 1

I Biot - Savart's law i de Sino dete dB = la s en conductor pą= R de = current carrying of any shape. Small element intre conducto r = position vector of point with respect to small element a I angle between de añ Mo= permeability of magnetic field. - * magnetic field due to wire of Short length B = 1 I [sina+Siup ] 2 (BB TAL I ---- B Ve 1.TR k..... / xt cent O2 o cent = 2BpQ t 2 Bes Becom => [tbCsuka sung) + un somatsu Sent = hot to be laban Bcant = him I was a lot + a varive] Blant = 2 Mo I [ 9 + 2 + - B cent = ñ (rar+52) 2 MOI Āra 762" ab - as bacca as 5ta= a Beent = 2 / 4 ore I x 96 Lcca a ~ da / B=4 peoI [ sinus tsa K ñų B = 2 . I x2 Ta