(a) Find the magnetic field at the center of a square loop, which carries a steady current I. Let R be the distance from center to side (Fig. 5.22). (b) Find the field at the center of a regular n-sided polygon, carrying a steady current I. Again, let R be the distance from the center to any side. (c) Check that your formula reduces to the field at the center of a circular loop, in the limit n → ∞.

Community Answer

Caleulate the has tenit magretic field at the centes of the squane 100P.U Se equelion 5.35 The magretic field CH a distunce: from a long straight wihe canying o ste4dy cusent I is als follows.B=(mu_(0)1)/(4x2)(sin theta_(2)-sin theta_(1))Here, theta_(1) and theta_(2) care the intitit and final angles,A steady cussent of I passing theova each side of the squethe loop and R be the distemce from centes to side.square has tolally fouk wines and each wise produces magnetic plels at the center of the square,B=4[(mu_(0)I)/(4xz)(sin theta_(2)-sin theta_(1))]In the given case, the initial and final arales ahe as follows:{:[theta_(2)=45^(@)],[theta_(1)=-45^(@)]:}The distance of the wire from the centes is, 2=Rsubstitute R Forz. 45^(@) fos theta_(1), and -45^(@) for theta_(2) in the equation B=4(mu_(0)I)/(4pi R)(sin 45^(@)-sin(-45^(@))) =(mu_(0)I)/(pi R)((1)/(sqrt2)+(1)/(sqrt2)) =(sqrt2mu_(0)I)/(pi R)The fore, the magnetic field at the centes of the sauare loor is (sqrt2mu_(0)I)/(pi R). Find the magnetic field at theb) center of a regulas n-sided polygon, carhying a steady cursen ... See the full answer