Question

Magnetic flux density is given as B =* = 6+ Problem [1] <15 points> on a surface given by r = 510,= = 48. Calculate the total flux o passing through this surface. For Problems 2 to 4: Figure shows a resistive loop with resistance of 2 Ohms. Magnetic flux density in this region is B = (2zł + 3xý)e ^. Calculate the current on this loop at t-0.1 seconds. 2 2 2 10

Answer 1

102 Given B - $2 (1) <o + Фz 7 g → It is in cylindrical coordinak. also given, 8=5 10 & -T/ do=0 z = 4 +8 * Total Flux Passing through the through the surface 8 = 88dš » $ = $42. $ + 9). Medz @ + fdød SI > $ - Sleman drdz + Oz $z odda) 8 since d 8 10 10 so 8 = 15 82 dr dz ht S z dr dz T-5 て=4825 2-4 & 20 dr $ = 7 A Sa zdz io 5 = = tem che si flor) → ♡ [04-15] (lo 10-ms] > 8

(2) = 2 x 48 x 0.693 8 = 13.0627 Wo Any Z R=22 2 10 2 X is since 30, Given, magnetic fleen density (3) B=(22 i + 3x g) ezt Loop in y-z plane ,so x=0 B=(22 åto) ezt Total flux passing through Loop $= S Bodšo =562.22tjâ • (dydz Â) See z dz dy). 22t = 22oe2t

1 2t $ = 20 12d2 dy y=2 2=2 C. = 284 (07-12) 2 -2t -2e 2 (10-2) * [ 36-41 e²* 8] * [32] ro +0 ēzt 256 At £=1 je c, =2 $ - 34.646 wbl As = 256 e 2 (3) Induced Emf in the loop E = - den 286 x d m at -2t =+256x2x E- = 512 ezt volt 乡

tha so, current in the loop 512 ezt R 3/1 = 256 e 2t 1- 2 * At t=1s i cussent excell be , -2x] 1 =256 e A - 256xe -2 I = 34.646 A ( 4 ) since , 3 = (2z î + gxg) 72 + is decreasing so neill since, In x-direction 8 .is idth time from Lena's hace , current be in anticlockwise - direction, so that it will help to increase the B. Answer:- Anticlock weise direction.