Question

d) Three point charges are located as shown in Figure 2 (see page 6). All three charges are
a distance a from the origin.
i) Calculate the dipole moment for this charge configuration [2]
ii) By calculating the first two terms of the multipole expansion for this cofiguration,f ind
an approximate expression for the scalar potential of this cofiguration. Express your
result in spherical polar coordinates. [5]
iii) Hence provide an approximate expression for the electrical field, E, for this charge
confiuration. Express your result in spherical polar coordinates. [5]
Hint - You may find the following expression for the gradient in spherical polar coordi-
nates useful,

1 af r sin oo- дг 5 Z +q a У a a q q Figure 2: Point charge distribution

Answer 1

the dipole moment,expression for the scalar potential and also the expression for the electrical field, E have been calculated for the charge configuration...
). E > 9 9 49 Solution ③ To find approximate fuld such that (roxa) so to find ☆ 1 -q y potential and choose gradient, here in the need to dipole and monopole terme in expansion that the two lawent Orden. a monopole i -q=Qtot monopole = -q Auror the dipole. Ř can be represented as, P-Er wi aqlaž)-q (ay) +qla) Pagaż To connect to dephenical, P qa C Caso n - Sino a

In this, the dipole, =(-q) a (-²) ô ) P =+qa (cone & – Sin e So, p. 7 – – qa Coro V dip - qacaro Hei Erz So, the appoxianate expression for scelare potential on V (2) at co - 2 + qacord) the decleic field E -- ming a 2 2 2 2 2 P ara ello - synonym

& feno ôs] que (* ) which represents like point charge and it is reasonable uu