In the picture there is a point charge and two conducting spherical shells conce

Question

In the picture there is a point charge and two conducting spherical shells concentric about the charge. The point charge has a charge of -3.5 uC. The inner spherical shell has an inner radius sub 1i =0.14 m and r sub 1o = 0.16 m, and has no net charge. The outer spherical shell has an inner radius of r sub 2i=0.34 m and r sub 2o = 0.36 m, and it has a net charge of +1.5 uC. i) What is the charge on the INNER SURFACE of the inner spherical shell? ii) Use Gauss's law to find the electric field at a point r=0.24 m from the center of the spheres. iii) What is the charge on the OUTER SURFACE of the outer spherical shell? iv) Use Gauss's law to find the electric field at a point r = 0.50 m from the center of the spheres.

Explanation / Answer

by symmetry, the field is uniform with respect to location parallel to the sheets and is normal to the sheet surface. so ?E*dA = E*A; this equals the total charge enclosed in a volume of area A E*A = q/e0 = q/(A*e0) q/A = s so E = s/e0 so the answer to a) is (s1 + s2 + s3 + s4)/e0 = 5*10^-6/e0 N/C For b) the point is between the sheets. Place the gaussian surface so that the one end is outside the sheets and the other at the specified location between the sheets. Since we know the field on the outside surface the surface integral of field is 5*10^-6/e0 + E = (s1 + s2)/e0 E = (-5*10^-6 - 6.00*10^-6 + 5.00*10^-6)/e0 In the middle of the right hand sheet, just add s3 to the right hand side (charge enclosed) 5*10^-6/e0 + E = (s1 + s2 + s3)/e0

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