Question 2
(a)
Define electric potential at
a point. [2]
(b)
An isolated metal sphere is charged to a potential V.
The charge on the sphere is q.
The charge on the
sphere may be considered to act as a point charge at the centre of the sphere.
The variation with
potential V of the charge q
on the sphere is shown in Fig. 5.1.
Fig. 5.1
Use Fig. 5.1 to
determine
(i)
the radius of the sphere, [2]
(ii)
the energy required to increase the potential of the sphere from
zero to 24 kV. [3]
(c)
The sphere in (b) discharges by causing
sparks when the electric field strength at the surface of the sphere is greater
than 2.0 × 106 V m-1.
Use your answer in (b)(i)
to calculate the maximum potential to which the sphere can be
charged. [3]
Reference: Past Exam Paper – November 2014 Paper 43 Q5
Solution:
(a)
The electric potential at a point is defined as the work
done / energy in moving unit positive charge from infinity (to the point)
(b)
(i)
V = q /
4πε0r
{from the
graph,} at 16 kV, q = 3.0 × 10–8 C
{r = q /
4πε0V}
r = (3.0 ×
10–8) / (4π × 8.85 × 10–12 × 16 × 103) C1
r = 1.69 ×
10–2 m (allow 2 s.f.) A1
(ii)
The energy
is represented by the area ‘below’ line
{Energy =
area of triangle between V = 0 kV to V = 24 kV}
{when V =
24 kV, q = 4.5 × 10–8 C}
Energy = ½
qV
Energy = ½
× 24 × 103 × 4.5 × 10–8
Energy =
5.4 × 10–4 J
(c)
since V = q
/ 4πε0r and E = q / 4πε0r2 giving Er = V (or V = E/r)
{The maximum
electric fields strength at which the sphere can be charged is E = 2.0 × 106 V m-1.}
2.0 × 106
× 1.7 × 10–2 = V
V = 3.4 × 104
V
