Question

A circular thin wire loop of radius a=37.2 cm and total resistance R=0.186 12 is positioned in the (xy)-plane, where it is exposed to the external (applied) uniform magnetic field directed along the z-axis. Over some period of time t, the z-component of that field varies as Bextz(t)=Bo – at + ßta, where Bo=6.68 T, a=60.727 T/s and ß=69.008 T/s2. Right at the geometrical center of the loop circle, there is a very accurate magnetometer that can detect the difference between the actually measured and the applied magnetic fields. It will thus measure the induced magnetic field that would be generated by the current induced in the wire loop. Find what would the measurement of the z-component Bindz of the induced magnetic field be at time t=0.255 s: G. Bind-=

Answer 1

E Criven a= 37.2cm -01872m az I Resistance FR = 0.1862 2 Bent (A) = Bordt + + Bt2 sy Z where Bo = 6.685 d=60072 7 T/s 8 = 6900087/24 * Due to external magnetic field, these will be emf induced in the loop. >> E = do at dBA dt E = d{(60-28+p+3) 1992 aasta 0 -0+23+) ta2ld-2Bt) E = 70

(2) Due to this in the loop. induced Emf, there will be cussent flow nal ( 2- 28t) R [ cerere R I E By this this Induced current, there will be induced magnetic field at the centre of hoop: llora(9 - 28+) → B 29 Rx za ind lo 1 z ind Mortal 0-28+) This will be B z 2R measured by the magnetometer • At t=0.255 see Bind 470x107x * x 0.372 (60.72 - 2 x 69-008x 0.255 2 x o. 186 und 3) B. .1007.72 x 40 107 T since IT = 104 G So, B Bind = 1007.72x107xion ind 3 Bha = 1.008 G This is the required 2 misrel ez