474
11 Electrostatics
Fig. 11.10
11.55 (a) The electric field on the surface of a thin spherical shell of radius 0.5 m
is measured to be 800 N/C and points radially towards the centre of the
sphere. What is the net charge within the sphere’s surface?
(b) An electric field of 120 N/C points down over a football field. Calculate
the surface charge density on the field.
(c) What would be the total electric flux if the field is 100×75 m 2 .
11.56 (a) Using Gauss’ law derive Coulomb’s formula for the electric field due to
an isolated point charge q.
(b) A positive charge Q is uniformly distributed in a non-conducting sphere
of radius R. Calculate the electric flux passing through the spherical
surface of radius r concentric with the sphere for (i) r < R; (ii) r > R.
11.57 How is electric flux related to the electric field E? How is the total electric
flux over a closed surface related to the charge enclosed within the surface?
A thin spherical shell of radius R 1 carries a total charge Q 1 that is uniformly distributed on its surface. A second, larger concentric thin shell of
radius R 2 carries a charge Q 2 also uniformly distributed over the surface of
the shell. Use Gauss’ law to find the electric field in the regions.
(a) r < R 1 ,
(b) R 1 < r < R 2 , and
(c) R 2 < r .
The electric charges are such that Q 1 > 0 and the electric field is zero for
r > R 2 . Find the ratio Q 1 /Q 2 .
11.58 Two insulated spheres of radii 1 and 3 cm at a considerable distance apart are
each charged positively with 3 × 10 −8 C. They are brought into contact and
separated by the same distance as before. Compare the forces of repulsion
before and after contact.
[Northern Universities of UK]
11.59 What is the maximum charge that can be given to a sphere of diameter 10 cm
if the breakdown voltage of air is 2 × 10 4 V/cm.
11.60 (a) Show that the capacitance, C, of a conducting sphere of radius a is given
by C = 4πε 0 a.
(b) Two isolated conducting spheres, both of radius a, initially carry charges
of q 1 and q 2 and are held far apart. The spheres are connected together
by a conducting wire until equilibrium is reached, whereupon the wire
11 Electrostatics
Fig. 11.10
11.55 (a) The electric field on the surface of a thin spherical shell of radius 0.5 m
is measured to be 800 N/C and points radially towards the centre of the
sphere. What is the net charge within the sphere’s surface?
(b) An electric field of 120 N/C points down over a football field. Calculate
the surface charge density on the field.
(c) What would be the total electric flux if the field is 100×75 m 2 .
11.56 (a) Using Gauss’ law derive Coulomb’s formula for the electric field due to
an isolated point charge q.
(b) A positive charge Q is uniformly distributed in a non-conducting sphere
of radius R. Calculate the electric flux passing through the spherical
surface of radius r concentric with the sphere for (i) r < R; (ii) r > R.
11.57 How is electric flux related to the electric field E? How is the total electric
flux over a closed surface related to the charge enclosed within the surface?
A thin spherical shell of radius R 1 carries a total charge Q 1 that is uniformly distributed on its surface. A second, larger concentric thin shell of
radius R 2 carries a charge Q 2 also uniformly distributed over the surface of
the shell. Use Gauss’ law to find the electric field in the regions.
(a) r < R 1 ,
(b) R 1 < r < R 2 , and
(c) R 2 < r .
The electric charges are such that Q 1 > 0 and the electric field is zero for
r > R 2 . Find the ratio Q 1 /Q 2 .
11.58 Two insulated spheres of radii 1 and 3 cm at a considerable distance apart are
each charged positively with 3 × 10 −8 C. They are brought into contact and
separated by the same distance as before. Compare the forces of repulsion
before and after contact.
[Northern Universities of UK]
11.59 What is the maximum charge that can be given to a sphere of diameter 10 cm
if the breakdown voltage of air is 2 × 10 4 V/cm.
11.60 (a) Show that the capacitance, C, of a conducting sphere of radius a is given
by C = 4πε 0 a.
(b) Two isolated conducting spheres, both of radius a, initially carry charges
of q 1 and q 2 and are held far apart. The spheres are connected together
by a conducting wire until equilibrium is reached, whereupon the wire