Question

There is a linear homogeneous electric charge, along the semicircle of radius R (see figure below).

Answer 1

\[\lambda _{r} = \lambda _{0} = constant \]
\[\lambda _{0} : charge density \]
\[p = 2*R*Q / \pi \]
A) Prove that the total charge is \[Q = \lambda _{0} * \pi* R\]

B) Prove that the dipole moment from the coordinates origin , can be calculated with
the expresion

Answer 2

NOTE: The expresion of the point B) is p = 2*R*Q / \pi . Prove that you can calculate de dipole moment like this

Answer 3

hey so A) charge density is constant

Answer 4

you know that dq = lamba dl
and since lambda is constant we can do
q=lambda * lenth
length here is the top half circumference of the circle therefore
q=lambda*pi * r

Answer 5

now the dipole momeny

Answer 6

oh umm if they want some more clear notation then