A solild plastic sphere of radius R1 -8.00 cm is concentric with an aluminum sph

Question

A solild plastic sphere of radius R1 -8.00 cm is concentric with an aluminum spherical shell with inner radius R2 14.0 cm and outer radius R 17.0 cm (see figure below). Electric field measurements are made at two points: At a radial distance of 34.0 cm from the center, the electric field has magnitude 8.30 x 10 N/C and is directed radially outward, and at a radial distance of 12.0 cm from the center, the electric field has magnitude 1.95 × 104 N/C and is directed radially inward what are the net charges on the following? Plastic Aluminum (a) the plastic sphere the aluminum spherical shell (c) What are the charges on the inner and outer surfaces of the aluminum spherical shell nner outer

Explanation / Answer

Solution,

A)

Electric field, E = kQ/R^2

-(1.95 x 10^4) = (9 x 10^9)(Q)/(0.12)^2

Q = - 3.12 x 10^-8 C

B)

8300 = (9 x 10^9)Q/(0.34)^2

Q = 1.07 x 10^-7 C

Q_Al + Q_P = 1.07 x 10^-7

Q_Al = (1.07 x 10^-7) + (3.12 x 10^-8) = 1.38 x 10^-7 C

C)

Q_inner = 3.12 x 10^-8 C

Q_outer = 1.07 x 10^-7 C

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