Question

(b) Find the quadrupole moment tensor $Q_{ij}$ for the four charges shown below: +q (0,0,+d) -2q +q (0,0,-d) (c) Find the electric potential for the quadrupole charge distribution shown above Point P (d) Find the following terms for the quadrupole charge distribution: 1) $k \int \frac{\rho(\vec{r'})}{r} dv' $ 2) $k \int \frac{\vec{r'} \cdot \vec{r}}{r^3} \rho(\vec{r'}) dv' $ Note $k = \frac{1}{4\pi\epsilon_0}$

          (b) Find the quadrupole moment tensor $Q_{ij}$ for the four charges shown below:
+q
(0,0,+d)
-2q
+q
(0,0,-d)
(c) Find the electric potential for the quadrupole charge distribution shown above
Point P
(d) Find the following terms for the quadrupole charge distribution:
1) $k \int \frac{\rho(\vec{r'})}{r} dv'
$
2) $k \int \frac{\vec{r'} \cdot \vec{r}}{r^3} \rho(\vec{r'}) dv'
$
Note $k = \frac{1}{4\pi\epsilon_0}$

(b) Find the quadrupole moment tensor Qij for the four charges shown below:
+q
(0,0,+d)
-2q
+q
(0,0,-d)
(c) Find the electric potential for the quadrupole charge distribution shown above
Point P
(d) Find the following terms for the quadrupole charge distribution:
1) k ∫(ρ(r⃗'⃗))/(r) dv'
2) k ∫(r⃗'⃗·r⃗)/(r^3)ρ(r⃗'⃗) dv'
Note k = (1)/(4πϵ0)

Added by Jose Antonio W.

Physics SAT Subject Test

Robert Jansen, Greg Young 2nd Edition

Chapter 24

Instant Answer

Solved by Expert Dinesh Chand Jangid

Step 1

We have four charges arranged as follows: - Charge +q at position (0, +d) - Charge -2q at position (0, 0), the origin - Charge +q at position (0, -d) - Point P is at some distance r from the origin at angle θ Show more…

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solve B) , C) and D) 1, 2 step by step bFind the quadrupole moment tensor Q for the four charges shown below: (0.0,+d Point P (0,0,-d) cFind the electric potential for the quadrupole charge distribution shown above dFind the following terms for the quadrupole charge distribution: 2)k o(r)dv Note k= 480