Q is the monopole moment,
P vector is the dipole moment,
Qjk is the quadrupole moment.
I understand how to compute the dipole and monopole but the
quadrupole is a bit over my head. They use electric dipole
expansion
Homework Answers
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Q is the monopole moment,
P vector is the dipole moment,
Qjk is the quadrupole moment....
OEM . . ., 2. A world with a quadrupole (20 pts.) (a) We have two...
OEM . . ., 2. A world with a quadrupole (20 pts.) (a) We have two positive point charges, + at two diagonal corners of a square (sta, ta, 0) and two minus charges - at the two other diagonals of a square (ta, Fa, 0). Using linear superposition, find the electric potential ( in a Taylor expansion, assuming 171a. What is the leading non-zero term? (b) Given the charges as specified in (a), evaluate explicitly the monopole, dipole, and...
2. Quadrupole potential Given a charge distribution p(7)= q8(f-ai)+qô(f+ai)- qô(f-a2) - qố (f+ā2), where q >...
2. Quadrupole potential Given a charge distribution p(7)= q8(f-ai)+qô(f+ai)- qô(f-a2) - qố (f+ā2), where q > 0 and ai and a2 given in Cartesian coordinates by ai = (a,0,0) and ā2 = (0, a,0) with a > 0. are a) Calculate the resulting potential p and the electric field b) What is the electrostatic energy of the charge distribution (without the self-energy contri- bution of the point charges themselves)? c) Determine the dipole moment p= f d*r'rp(F) and the quadrupole...
1) In class, we worked out the multipole expansion for the potential of a system of...
1) In class, we worked out the multipole expansion for the potential of a system of two charges q1 and q2, distances di and d2 from the origin. For r » di, d2, the first three terms of the expansion looked like: 4πε0 I also claimed that if we generalized things to systems with lots of charge, the multipole potential out to the quadrupole term would look like V(X) = where q is the monopole moment, p is the dipole...
A dipole is oriented along the x axis. The dipole moment is p (= qs). (Assume...
A dipole is oriented along the x axis. The dipole moment is p (= qs). (Assume the center of the dipole is located at the origin with positive charge to the right and negative charge to the left.) (a) Calculate exactly the potential V (relative to infinity) at a location x, 0, 0 on the x axis and at a location 0, y, 0 on the y axis, by superposition of the individual 1/r contributions to the potential. (Use the...
What is the magnitude of the dipole moment for the two charges, q, spaced a distance...
What is the magnitude of the dipole moment for the two charges, q, spaced a distance s apart? Express your answer with the appropriate units. Review An electric dipole is formed from two charges, ±q, spaced a distance s apart. The distance s is small compared to 10 cm. The dipole is at the origin, and the dipole moment p points in the y- direction. The electric field strength at the point P : (x, y ,(0 cm, 10 cm)...
An electric dipole consists of a negative charge- located at (0,-) and a positive charge +q...
An electric dipole consists of a negative charge- located at (0,-) and a positive charge +q located at (0, +3). The dipole moment p is defined as a vector of magnitude qs directed from the negative charge of the dipole to the positive charge of the dipole. (a) Show that the net force exerted by the dipole on a charge +Q located on the r-axis at a distance r from the dipole is given by: s 2 -3/2 F- r"...
Two charges (dipole) of +q = +6.00 μC and −q = −6.00 μC along the y-axis,...
Two charges (dipole) of +q = +6.00 μC and −q = −6.00 μC along
the y-axis, separated by 3.00 m, as shown in the figure below.
Point P is located 4.00 m directly to the right of the positive
charge, as shown. The origin is located halfway between the
charges.
(a) At point P (test point), sketch and label the electric field
E+ due to the positive charge +q, and the electric field E - due to
the negative charge...
An electric dipole is formed from two charges, ±q, spaced a distance s apart. The distance s...
An electric dipole is formed from two charges, ±q, spaced a distance s apart. The distance s is small compared to 10 cm. The dipole is at the origin, and the dipole moment p⃗ points in the y-direction. The electric field strength at the point P:(x,y)=(0cm,10cm) is 320 N/C 1. The two charges, ±q, are spaced a distance s apart. The dipole moment p⃗ is rotated 90∘ so it points in the +x-direction. What is the electric field E⃗ at the point P:(x,y)=(0cm,10cm) ? Give your...
Problem 1: Dipole moment. We have a sphere of radius R with a uniform surface charge...
Problem 1: Dipole moment. We have a sphere of radius R with a uniform surface charge density +ao over the northern hemisphere, and -oo over the southern hemisphere (oo is a positive constant). There are no other charges present inside or outside the sphere. Compute the dipole moment p of this charge distribution assuming the z-axis is the symmetry axis of the distribution. Does p depend on your choice of origin? Why or why not? Are any components of p...
FIG. 2. Setup of Exercise 3 Exercise 3 The electrostatic potential of an electic dipole moment...
FIG. 2. Setup of Exercise 3 Exercise 3 The electrostatic potential of an electic dipole moment d located at the origin takes the following form d-T Tr where r is the vector joining the origin to the point X (7 is called the "position vector" in the textbook). See Fig. 2 (i) Chosing the z axis to be aligned with the electric dipole moment, express φ in terms of cartesian, cylindrical, (ii) The electric field is obtained from E-- Compute...
OEM . . ., 2. A world with a quadrupole (20 pts.) (a) We have two positive point charges, + at two diagonal corners of a square (sta, ta, 0) and two minus charges - at the two other diagonals of a square (ta, Fa, 0). Using linear superposition, find the electric potential ( in a Taylor expansion, assuming 171a. What is the leading non-zero term? (b) Given the charges as specified in (a), evaluate explicitly the monopole, dipole, and...
2. Quadrupole potential Given a charge distribution p(7)= q8(f-ai)+qô(f+ai)- qô(f-a2) - qố (f+ā2), where q > 0 and ai and a2 given in Cartesian coordinates by ai = (a,0,0) and ā2 = (0, a,0) with a > 0. are a) Calculate the resulting potential p and the electric field b) What is the electrostatic energy of the charge distribution (without the self-energy contri- bution of the point charges themselves)? c) Determine the dipole moment p= f d*r'rp(F) and the quadrupole...
1) In class, we worked out the multipole expansion for the potential of a system of two charges q1 and q2, distances di and d2 from the origin. For r » di, d2, the first three terms of the expansion looked like: 4πε0 I also claimed that if we generalized things to systems with lots of charge, the multipole potential out to the quadrupole term would look like V(X) = where q is the monopole moment, p is the dipole...
What is the magnitude of the dipole moment for the two charges, q, spaced a distance s apart? Express your answer with the appropriate units. Review An electric dipole is formed from two charges, ±q, spaced a distance s apart. The distance s is small compared to 10 cm. The dipole is at the origin, and the dipole moment p points in the y- direction. The electric field strength at the point P : (x, y ,(0 cm, 10 cm)...
An electric dipole consists of a negative charge- located at (0,-) and a positive charge +q located at (0, +3). The dipole moment p is defined as a vector of magnitude qs directed from the negative charge of the dipole to the positive charge of the dipole. (a) Show that the net force exerted by the dipole on a charge +Q located on the r-axis at a distance r from the dipole is given by: s 2 -3/2 F- r"...
Two charges (dipole) of +q = +6.00 μC and −q = −6.00 μC along
the y-axis, separated by 3.00 m, as shown in the figure below.
Point P is located 4.00 m directly to the right of the positive
charge, as shown. The origin is located halfway between the
charges.
(a) At point P (test point), sketch and label the electric field
E+ due to the positive charge +q, and the electric field E - due to
the negative charge...
Problem 1: Dipole moment. We have a sphere of radius R with a uniform surface charge density +ao over the northern hemisphere, and -oo over the southern hemisphere (oo is a positive constant). There are no other charges present inside or outside the sphere. Compute the dipole moment p of this charge distribution assuming the z-axis is the symmetry axis of the distribution. Does p depend on your choice of origin? Why or why not? Are any components of p...
FIG. 2. Setup of Exercise 3 Exercise 3 The electrostatic potential of an electic dipole moment d located at the origin takes the following form d-T Tr where r is the vector joining the origin to the point X (7 is called the "position vector" in the textbook). See Fig. 2 (i) Chosing the z axis to be aligned with the electric dipole moment, express φ in terms of cartesian, cylindrical, (ii) The electric field is obtained from E-- Compute...
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