(20%) Problem 4: hollow non-conducting spherical shell has immer radius R/-5 cm
ID: 1317065 • Letter: #
Question
(20%) Problem 4: hollow non-conducting spherical shell has immer radius R/-5 cm and ouler radius R2-17 cm. charge Q--35 nC lies athe center ofthe shell. The shell cames a spherically symmetric charge density -Ar lor Rre: R2 lhal increases linearly with radius, where A-2/uc/nt Randomized Variables Q--35 nC R2 17 cm 25% Part a wnle an equalon lor lhe radial electric held in lhe regon r R/ m lems of posilive direction as oulward. r, and Coulomb's constan! k You mev lake lhe Grade Summary Dcductions Potcntial E) 7 8 9 4 5 6 Submissions Attempts remaini (4%, per attemt) detailed view (x al i1n R2 BACKSPACExplanation / Answer
a) at, r<R1, Qin = Q
E = k*Q/r^2 <<<<<<<<---------Answer
b) at r = 0.5*R1
E = k*Qin/r^2
= k*Q/(0.5*R1)^2
= 4*k*Q/R1^2
= -4*9*10^9*35*10^-9/0.05^2
= -5.04*10^5 N/c <<<<<<<<---------Answer
c) rho = dQ/dV
dQ = rho*dV
= (A*r)*(4*pi*r^2)*dr
= (A*4*pi*r^3)*dr
Qin = Q + inegral dQ
= Q + inegral (A*4*pi*r^3)*dr
= Q + A*pi*r^4
= Q + A*pi*( (R1+R2/2)^4 - R1^4)
= -35*10^-9 + 21*10^-6*( (0.05+0.17)/2)^4 - 0.05^4)
= -32.06*10^-9 C
r = 0.5*(0.05+0.17)
= 0.11 m
E = k*Qin/r^2
= -9*10^9*32.06*10^-9/0.11^2
= -2.38*10^+4 N/c <<<<<<<<---------Answer
d) Qin = Q + inegral dQ
= Q + inegral (A*4*pi*r^3)*dr
= Q + A*pi*r^4
= Q + A*pi*( R2^4 - R1^4)
= -35*10^-9 + 21*10^-6*( 0.17^4 - 0.05^4)
= -17.6*10^-9 C
r = 2*R2
= 2*0.17
= 0.34 m
E = k*Qin/r^2
= -9*10^9*17.6*10^-9/0.34^2
= -1.37*10^3 N/c <<<<<<<<---------Answer
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