Consider a spherical insulator of radius R_(a) with uniform volume charge density of total
charge Q_(1)=+2mC. This sphere is placed concentric within a conducting spherical
shell of inner radius R_(b) and outer radius R_(c). The outer spherical shell has a net charge
Q_(2)=-5mC. A dielectric material with permittivity epsi lon=20epsi lon_(0) and no net charge fills
the space between the two spheres. (Sect. 22.4, 23.2, 24.6)
a. What is the volume charge density of the insulating sphere?
b. What is the surface charge density on the inner and outer surfaces of the
spherical shell?
c. In terms of the variables provided, use Gauss' Law to derive expressions for the
electric field E(r) in the four regions
i. V(r->infty )=Delta V_(I)=V(0)-V(R_(a))Delta V_(II)=V(R_(a))-V(R_(b))Delta V_(III)=V(R_(b))-V(R_(c))Delta V_(IV)=V(R_(c))-V(infty )E(r)rR_(c)
d. In terms of the variables provided, derive expressions for the difference in
electrical potential between the surfaces in the four regions, using V(r->infty )=
0 as the reference.
i. Delta V_(I)=V(0)-V(R_(a))
ii. Delta V_(II)=V(R_(a))-V(R_(b))
iii. Delta V_(III)=V(R_(b))-V(R_(c))
iv. Delta V_(IV)=V(R_(c))-V(infty )
e. Sketch a graph of E(r) vs. r (i.e. a line plot) extending through the four regions.
i. On this graph, for region ii, add an extra line indicating the electric field if
the dielectric material were removed. Perhaps use a dashed line so I can
see the difference.R_(b)
iv. R_(c)
d. In terms of the variables provided, derive expressions for the difference in
electrical potential between the surfaces in the four regions, using V(r->infty )=
0 as the reference.
i. Delta V_(I)=V(0)-V(R_(a))
ii. Delta V_(II)=V(R_(a))-V(R_(b))
iii. Delta V_(III)=V(R_(b))-V(R_(c))
iv. Delta V_(IV)=V(R_(c))-V(infty )
e. Sketch a graph of E(r) vs. r (i.e. a line plot) extending through the four regions.
i. On this graph, for region ii, add an extra line indicating the electric field if
the dielectric material were removed. Perhaps use a dashed line so I can
see the difference.R_(a)
iii. R_(b)
iv. R_(c)
d. In terms of the variables provided, derive expressions for the difference in
electrical potential between the surfaces in the four regions, using V(r->infty )=
0 as the reference.
i. Delta V_(I)=V(0)-V(R_(a))
ii. Delta V_(II)=V(R_(a))-V(R_(b))
iii. Delta V_(III)=V(R_(b))-V(R_(c))
iv. Delta V_(IV)=V(R_(c))-V(infty )
e. Sketch a graph of E(r) vs. r (i.e. a line plot) extending through the four regions.
i. On this graph, for region ii, add an extra line indicating the electric field if
the dielectric material were removed. Perhaps use a dashed line so I can
see the difference.r
ii. R_(a)
iii. R_(b)
iv. R_(c)
d. In terms of the variables provided, derive expressions for the difference in
electrical potential between the surfaces in the four regions, using V(r->infty )=
0 as the reference.
i. Delta V_(I)=V(0)-V(R_(a))
ii. Delta V_(II)=V(R_(a))-V(R_(b))
iii. Delta V_(III)=V(R_(b))-V(R_(c))
iv. Delta V_(IV)=V(R_(c))-V(infty )
e. Sketch a graph of E(r) vs. r (i.e. a line plot) extending through the four regions.
i. On this graph, for region ii, add an extra line indicating the electric field if
the dielectric material were removed. Perhaps use a dashed line so I can
see the difference.
1. Consider a spherical insulator of radius Ra with uniform volume charge densitv of total
charge Q, = +2 mC. This sphere is placed concentric within a conducting spherical shell of inner radius Rp and outer radius Rc: The outer spherical shell has a net charge Q2 = --5 mC. A dielectric material with permittivity e = 20eo and no net charge fills the space between the two spheres.(Sect.22.4,23.2,24.6)
a. What is the volume charge density of the insulating sphere?
b. What is the surface charge density on the inner and outer surfaces of the Spherical shell?
c. In terms of the variables provided,use Gauss' Law to derive expressions for the
electric field E(r) in the four regions
i.r<Ra ii.Ra<r<Rp iii. Rp<r<Rc iv. Rc<r
d. In terms of the variables provided,derive expressions for the difference in electrical potential between the surfaces in the four regions,using V(r- co)= O as the reference.
i. V=V(O)-V(Ra) ii. 4Vu=V(Ra)-V(Rb) iii.V=V(Rp)-V(Rc) iv.Vv=VR-V(
e. Sketch a graph of E(r) vs.r (i.e. a line plot) extending through the four regions
i. On this graph, for region ii, add an extra line indicating the electric field if the dielectric material were removed. Perhaps use a dashed line so I can see the difference.