What Are the Monopole and Dipole Moments of a Two Charge System?

[stunner5000pt]

Two point charges 3q and iq are spearated by distance a as in the diagram. Find the monopole, dipole moments and the approximate potential at large (in spherical coords including both dipole and monopole contributions)

monopole moment is sum of charges $3q \hat{k} + qa \hat{k} = q(a+2) \hat{k}$

dipole moment is (assume that the origin is located half way between the two cahrges

then
$$p= 3q \frac{a}{2} \hat{k} + (-q}\frac{a}{2} \hat{k} = 2qa \hat{k}$$

also
$$\overline{p} = p + qa\hat{k}$$
$$\overline{p} = qa \hat{k}$$
is this correct?

where di i got wrong? with the transofmration of coordinates? With the way i calculated p?? When i calculate the potential the dipole moment will point radially in the z direction hence [itex] \hat{k} = \hat{r} \cos\theta [/tex]

thank you for your help and responses!

 

[Meir Achuz]

Two point charges 3q and iq are spearated by distance a as in the diagram. Find the monopole, dipole moments and the approximate potential at large (in spherical coords including both dipole and monopole contributions)

monopole moment is sum of charges $2q \hat{k} + qa \hat{k} = q(a+2) \hat{k}$

dipole moment is (assume that the origin is located half way between the two cahrges

then
$$p= 3q \frac{a}{2} \hat{k} + (-q}\frac{a}{2} \hat{k} = 2qa \hat{k}$$

also
$$\overline{p} = p + qa\hat{k}$$
$$\overline{p} = qa \hat{k}$$
is this correct?

where di i got wrong? with the transofmration of coordinates? With the way i calculated p?? When i calculate the potential the dipole moment will point radially in the z direction hence [itex] \hat{k} = \hat{r} \cos\theta [/tex]

thank you for your help and responses!

1. You seem to mean q and 2q in the first line. There should be no \hat k and no a in the monopole moment.
2. The usual convention for a charged object is to pick the origin so that the dipole moment is zero. I have not seen the diagram, so maybe you are told where to pick the origin.

 

[stunner5000pt]

oops

here is the diagram

pick a zer dipole moment... how in this case

 

[stunner5000pt]

1. You seem to mean q and 2q in the first line. There should be no \hat k and no a in the monopole moment.
2. The usual convention for a charged object is to pick the origin so that the dipole moment is zero. I have not seen the diagram, so maybe you are told where to pick the origin.

but isn't hte dipole moment a vector?/

 

[Meir Achuz]

here is the diagram

pick a zer dipole moment... how in this case

For your diagram, the charge is 3q-q=2q.
With the origin given at the postionf of the -q charge, the dipole moment is
$${\bf p}=3q{\bf\hat z}$$.