Gauss' Law with Calculus Video Lessons

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# Problem: A hollow non-conducting spherical shell has inner radius R1 = 8cm and outer radius R2 = 15 cm. A charge Q = 45 nC lies at the center of the shell. The shell carries a spherically symmetric charge density ρ = Ar for R1 &lt; r &lt;R2 that increases linearly with radius, where A= 29 μC/m4 What is the radial electric field at the point r = 2R2? Give your answer in units of kN/C.

###### FREE Expert Solution

Electric field:

E = kQ/r2

R1 = 8cm(1m/100cm) = 0.08m

R2 = 15 cm(1m/100cm) = 0.15 m

r = 2R2 = 2 × 15 cm(1m/100cm) = 0.30 m

Qpoint charge = - 45 nC(10-9C/1nC) = - 45 × 10-9 C

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###### Problem Details

A hollow non-conducting spherical shell has inner radius R= 8cm and outer radius R2 = 15 cm. A charge Q = 45 nC lies at the center of the shell. The shell carries a spherically symmetric charge density ρ = Ar for R1 < r <R2 that increases linearly with radius, where A= 29 μC/m4

What is the radial electric field at the point r = 2R2? Give your answer in units of kN/C.