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problem23_44

# University Physics with Modern Physics with Mastering Physics (11th Edition)

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23.44: a) (i) . 1 1 : - = - = < b a b a a r r kq r kq r kq V r r (ii) . 1 1 : - = - = < < b b b a r r kq r kq r kq V r r r (iii) , 0 : = V r r b since outside a sphere the potential is the same as for point charge. Therefore we have the identical potential to two oppositely charged point charges at the same location. These potentials cancel. b) - = = - = b a ab b b a a r r q πε V V r q r q πε V 1 1 4 1 0 and 4 1 0 0 c) . 1 1 1 4 1 1 1 4 : 2 2 0 0 r r r V r q πε r r r πε q r V E r r r b a ab b b a - = + = - - = - = < < d) From Equation (24.23): , 0 = E since V is zero outside the spheres. e) If the outer charge is different, then outside the outer sphere the potential is no
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Unformatted text preview: longer zero but is . ) ( 4 1 4 1 4 1 r Q q πε r Q πε r q πε V-=-= All potentials inside the outer shell are just shifted by an amount . 4 1 b r Q πε V-= Therefore relative potentials within the shells are not affected. Thus (b) and (c) do not change. However, now that the potential does vary outside the spheres, there is an electric field there: . 1 2 -= -+ ∂ ∂-= ∂ ∂-= q Q r kq r kQ r kq r r V E...
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