A hollow non-conducting spherical shell has inner radius R1−6cm and outer radius R2=15cm. A charge Q=35nC lies at the center of the shell. The shell carries a spherically symmetric charge density p=Ar for R1&lt;r&lt;R2 that increases linearly with radius, where A=19uCm4 Part (a) Write an equation for the radial electric field in the region r&lt;R1 in terms of Q, r, and Coulombs

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A hollow non-conducting spherical shell has inner radius R1−6cm and outer radius R2=15cm. A charge Q=35nC lies at the center of the shell. The shell carries a spherically symmetric charge density p=Ar for R1&amp;lt;r&amp;lt;R2 that increases linearly with radius, where A=19uCm4   Part (a) Write an equation for the radial electric field in the region r&amp;lt;R1 in terms of Q, r, and Coulombs

Bubich13 · Accepted Answer

(a) Er&amp;lt;R1=Kr2(b) E=9×109×(−35×10−9)(0.5×6×10−2)2=−3.5×105Nc(c) Assuming a spherical of radiusr=0.5(R1+R2)Enclosed charge is calculated as:a=Q+∫R1r×4×r2drq=−35nc+∫R1r19×10−6×4πr3dr⇒q=−35×10−9+[19×10−6×π×r4]R1r=−35×10−9+19π×10−6×(r4−R14)r=0.5×(0.6+0.15)m=0.105m and R1=0.06m∴q=−35×10−9+19π×10−6×(0.1054−0.064)=−28.52×10−9CApplying Graun&#039;s low E×4πr2=qE0⇒E=14πE0×qr2=9×109×(−28.52×10−9)(0.105)2E=−2.328×104NC(d) for r=R2⇒q=−35×10−9+19π×10−6×(0.154−0.064)=−5.56×10−9C∴E=1

Jeremy Merritt · Accepted Answer

(a) From Gauss low,&amp;nbsp;E(4πr2)=qevecleted/E0&amp;nbsp;E=1/4πE0a/r2=kQ/r2&amp;nbsp;(b)&amp;nbsp;r=0.5R1&amp;nbsp;E=kQ/(0.5R1)2=(9×109)(−35×10−9)(0.5×7×10−2)2&amp;nbsp;=−257.14KN/C&amp;nbsp;(c)&amp;nbsp;r=0.5(R1+R2)&amp;nbsp;Qtotal=q/point+q/non-condiction&amp;nbsp;Vgauss=∫pdv0.5(R1+R2)&amp;nbsp;=A(4π)∫r3dr0.5(R1+R2)&amp;nbsp;=4πA(r4/4)0.070.13&amp;nbsp;=4π(21×10−6)4[(0.13)4−(0.07)4]&amp;nbsp;=1.725×10−8C&amp;nbsp;E=kq(R1+R2)2&amp;nbsp;=(9×109)(−35×10−9+1.725×10−8)(0.13)2&amp;nbsp;=−9.452KN/C&amp;nbsp;(d)&amp;nbsp;Vtotal=VPointcharge+Vnon-Conducting sphere&amp;nbsp;Vnon-conductor=∫R1R2Pdv&amp;nbsp;=4πA∫R1R2r3dr&amp;nbsp;=4π(21×10−6C)1/4(r4)0.070.19=&amp;nbsp;=8.44×10−8c&amp;nbsp;E=(9×109)×(−35×10−9c+8.44×10−8c)(2×0.19)2&amp;nbsp;E=3.078KN/C

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