Question

An 18.1v voltage source charges a capacitor that has circular plates with a radius of 4.4 cm, which is in series with a resistance of 6.36Ω. If the separation between plates is 9.35 mm, what is the magnetic field between the plates? 2.25 cm from the center when t = 2RC?
To achieve this, calculate the electric flux, consider that for a parallel plate capacitor the electric field E = ε0 σ and σ is the surface charge density σ = dq / dA, Calculate the charge on the capacitor q = (CVs) (1+ exp (-t / RC)) and its change over time, where C is the capacitance. Calculate the magnetic field in μT.

ÈCUT B + Vs

Answer 1

Azła² The It given The Parallel Plate capacitor with circulos Plate have Rodius a=4.4cm 0.044m area of Cross-sectional Plate plates d 9.35 X10m The sepration between the This capacitor connected with resistor R = 6.36 2 and constantly voltage source of voltage V.- 18. I Volt When the capacity connected with the source, the capacitor gets started charging through the Resistor. let CRT has cunent ľ at с 20+) has time t and capacitor ht) Chaage 2(+) at time t Apply KVL at loop ist IR d2 Vo - i i(t) = - 2 / dt de dt the (v.c-q) dt RC Both sides ㅗ integrate dt CV-q t=0 In (CV.-2 CN -9) t-o = -4/RC RC V + -Vot 2(t) с Rict) de evo-2 2 t de RC inley-2 CV-o -t/RC 20 -T/Rc CV-2 e & 8(t) = evo (1- و لحم at time t The voltage across the capacitor V(+) 26+) Vo (1-etec)

capacity Plates • E Ses The electic field in capacitor found using X "V(Me) - V(X2) Edx Xy Whexe Vivi) and Vixe) potente al ot Ki and H₂ xed E dx - E(0-0) Ed Xd → da - V8 ) + (0) kao d d V(xo) – V(x=d) = Ed V=Ed Potential difference E 00055 Copocitos The electric field in between the region at time t ps ARC Elt1 = Vo (1-é To find the magnetic field (B) use integral form of moywell equation de= Meade at ict) electric flux through the Circular of radius de = SEB Where de area Where ds = surface area element so Is = ds E = E PE= Ear de = Se ds - ES as

so a de at = 782 de dt = d1 à (Frax) quo letlee) } - * (0+ ks _+IRC But de et les e d dt dt dE dt Vo d RC so doe -T/RC Tr? Vo dR( dt e at t=aRC 6-2RC e RC T22 Vo -2 e dt T22 Vo d RC d RC so focê Mę doe dt 2 2 Vo e B 278= M & T82 No * B 2 = HE ġ Vo d RC dRc 2 BU M & r 2 Vo d RC e magnetic field at a

The capacitarce Plate capacitor is given by of circular c = E. A d So -2 e² Mon Blo) e2 = M Er Vo RA 2 Vo 2 dR E A d Mogi Vo é ² 2 Rña² SA - 7 -2 es 8(2) YA X 10 "x 2.25X16* (18.1) 2 636X310.044)? 2 at r=2.25 X10 m 56 -9 895.240 X10 Tesla B(A) 0.895 YIO Tesla The magnitude of the magnetic field at 8 = 2.25cm B(0-2.25 (T) = 0.895 MT is