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(Solved): An insulating sphere with radius a has a uniform charge density \rho . The sphere is not centered at ...
An insulating sphere with radius
ahas a uniform charge density
\rho . The sphere is not centered at the origin but at
vec(r)^(')=vec(b). Figure 2: (a) The electric field inside the sphere is given by
vec(E)=(\rho )/(3\epsi lon_(0))(vec(r)-vec(b)),(True,False) An insulating sphere of radius
Rhas a spherical hole of radius
alocated within its volume and centered a distance
bfrom the center of the sphere where
\rho vec(E)=vec(E)_(sphere ) vec(E)_((-\rho ))=(\rho )/(3\epsi lon_(0))vec(r) (-\rho )/(3\epsi lon_(0))(vec(r)-vec(b))=(\rho )/(3\epsi lon_(0))vec(b),( True, False )Ra|vec(r)-vec(b)|=\sqrt(r^(2) b^(2)-2rbcos\theta )vec(E)=vec(E)_(sphere ) vec(E)_((-\rho ))=(\rho )/(3\epsi lon_(0))vec(r) (-\rho a^(3))/(3\epsi lon_(0))((vec(r))-(vec(b)))/(|(vec(r))-(vec(b))|^(3)),( True,False )a (a cross section of the sphere is shown in figure 2 ). The solid part of the sphere has a uniform volume charge density \rho :
(b) The electric field inside the hole is constant and is given by :
vec(E)=vec(E)_(sphere ) vec(E)_((-\rho ))=(\rho )/(3\epsi lon_(0))vec(r) (-\rho )/(3\epsi lon_(0))(vec(r)-vec(b))=(\rho )/(3\epsi lon_(0))vec(b),( True, False )
(c) The electric field inside the sphere of radius R but outside the hole of radius a is not constant and is given by |vec(r)-vec(b)|=\sqrt(r^(2) b^(2)-2rbcos\theta ) :
vec(E)=vec(E)_(sphere ) vec(E)_((-\rho ))=(\rho )/(3\epsi lon_(0))vec(r) (-\rho a^(3))/(3\epsi lon_(0))((vec(r))-(vec(b)))/(|(vec(r))-(vec(b))|^(3)),( True,False )