Question

24: 15 points) consider a circular current loop of radius a in the x-y plane, which carries steady current l. Use Biot-Savart law to find the magnetic field strength anywhere on the z axis.

Answer 1

Solution - Given circular current loop of radius R= - a a Let us of find magnetic point Р h field at di which ý at height u Y I on z-axis from origin, current I flows in het anticlockwise direction. di at any Consider small segment of length applying Biot Sarart's Law - point and

dH I di x ar 40r2 Here, di = (Rdd) å 11 he + R2 ar 3131 ar hâč - Ra h+R? ma I de xan = 4 x 22 c X IR do I (R dd) ao haz R lag 4x (R+ b) h²+ R² (hão + Râz) 4* (R$h*) 912. radial rectors (ap) components among dn = IR do (Râz) 4* (R'++)372 Due to symmetry of loop, all cancel out each other Soi

ar = I R² â do 4* (R't ha)372 21 I R² do â H = fan is 46(e?+h*)! 0-0 ^ az 1 I R? (2x) 4* (R+h)92 IR² â 2 (Rth) IR? A az caus : H 2 (8²7 h2) 3/2 in clockwise direction then of current I flowes get (-âz) direction of magnetic we will point P. field at given radius Raa So. H duy I (a?) 2(a²+63)9/2