476
11 Electrostatics
11.66 A long cylinder of charge q has a radius a. The charge density within its
volume, ρ, is uniform (Fig. 11.11). Describe the form of the electric field
generated by the cylinder. Find the electric field strength at a distance r from
the axis of the cylinder in the regions (i) r > a and (ii) 0 < r < a.
If a non-relativistic electron moves in a circle at a constant distance R from
the axis of the cylinder, where R > a, find an expression for its speed.
[University of Manchester 2006]
Fig. 11.11
11.67 Consider an isolated non-conducting sheet with charge density σ . The electric field at 25 cm from the sheet is found to be 200 V/m, directed towards the
sheet. Calculate σ on the sheet. What electric field is expected at 2 cm from
its surface? How are the values of σ and E changed if a conducting sheet is
substituted.
11.2.3 Capacitors
11.68 Calculate the capacitance of a parallel plate capacitor of area A and thickness d if a dielectric slab of thickness t, area A and dielectric constant k is
inserted. How is the capacitance modified if a metal of thickness t is introduced?
11.69 Two capacitors C 1 and C 2 are connected in parallel and their combined
capacitance is measured as 9 μF. When they are combined in series their
capacitance is 2 μF. What are the individual capacitances?
11.70 Find the energy which may be stored in capacitors of 2 and 4 μF when taken
(a) singly, (b) in series and (c) in parallel when a potential difference of 100 V
is available.
[University of New Castle]
11.71 An air capacitor with plates 1 m 2 and 0.01 m apart is charged with 10 −6 C of
electricity. Calculate the change in energy which results when the capacitor
is submerged in oil of relative permittivity 2.0.
[University of Manchester]
11 Electrostatics
11.66 A long cylinder of charge q has a radius a. The charge density within its
volume, ρ, is uniform (Fig. 11.11). Describe the form of the electric field
generated by the cylinder. Find the electric field strength at a distance r from
the axis of the cylinder in the regions (i) r > a and (ii) 0 < r < a.
If a non-relativistic electron moves in a circle at a constant distance R from
the axis of the cylinder, where R > a, find an expression for its speed.
[University of Manchester 2006]
Fig. 11.11
11.67 Consider an isolated non-conducting sheet with charge density σ . The electric field at 25 cm from the sheet is found to be 200 V/m, directed towards the
sheet. Calculate σ on the sheet. What electric field is expected at 2 cm from
its surface? How are the values of σ and E changed if a conducting sheet is
substituted.
11.2.3 Capacitors
11.68 Calculate the capacitance of a parallel plate capacitor of area A and thickness d if a dielectric slab of thickness t, area A and dielectric constant k is
inserted. How is the capacitance modified if a metal of thickness t is introduced?
11.69 Two capacitors C 1 and C 2 are connected in parallel and their combined
capacitance is measured as 9 μF. When they are combined in series their
capacitance is 2 μF. What are the individual capacitances?
11.70 Find the energy which may be stored in capacitors of 2 and 4 μF when taken
(a) singly, (b) in series and (c) in parallel when a potential difference of 100 V
is available.
[University of New Castle]
11.71 An air capacitor with plates 1 m 2 and 0.01 m apart is charged with 10 −6 C of
electricity. Calculate the change in energy which results when the capacitor
is submerged in oil of relative permittivity 2.0.
[University of Manchester]