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Q1. MULTIPOLES - point charges You haye four point charges. Their location and charges in Cartesian...
You have four point charges. Their location and charges in Cartesian coordinates are: a positive charge,...
You have four point charges. Their location and charges in Cartesian coordinates are: a positive charge, 2q, located at (a,0,0), another charge -2q located at (-a,0,0), a 3rd charge -q located at (0,0,b), and finally a fourth charge +5q located at (0,0,-b) (a) What is the total charge, and dipole moment, of this distribution of charges? Use the methods of "the multipole expansion" (Griffiths section 3.4.1) to find a simple approximate formula for V(r,0) (in spherical coordinates!) valid at points...
d) Three point charges are located as shown in Figure 2 (see page 6). All three...
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...
Problem 8: Superposition of electric fields from several charges A charge Q is located at cartesian...
Problem 8: Superposition of electric fields from several charges A charge Q is located at cartesian coordinates (a,a). A charge Q is located at coordinates (a, -a) A charge is located at coordinates (-a, -a). Calculate the resultant electric field (E-field) at (a, Specify the magnitude and the direction of the electric field at (a, a) -a
1) three point charges are arranged as follows Q1=+q is located at (-a,0);Q2=+q is at (a,0)...
1) three point charges are arranged as follows Q1=+q is located at (-a,0);Q2=+q is at (a,0) Q3=-q (0,a) a)Calculate the electric field at the origin and the point (0,-a) b)there are two points in the field around the charges where the field around the charges where the field strength is zero.Approximately where will they be located?Sketch a vector diagram of the three field vectors at these points and show they add to zero. 2) q1=+q is located at the origin...
The following diagram shows 3 point charges and their coordinates on a cartesian grid For the...
The following diagram shows 3 point charges and their coordinates on a cartesian grid For the net electric field to be zero at P, what coordinates would a -5.0q charge need to be placed? P (3 m, 2 m) Q3 +1.0q (0 m ,2 m) Q1 Q2 +2.0q (0 m ,0 m -3.0q (3 m,0 m
We observe two point charges in the yz-plane: one of them has charge 2q and is located in (x,y,z)-(0,0,a) and the other...
We observe two point charges in the yz-plane: one of them has charge 2q and is located in (x,y,z)-(0,0,a) and the other has a charge of -3q and is located in (x,y,z)-(0,b,a) a) Calculate the dipole moment p, and p, for the two charges around (0,0,0), and sketch for a-2, b-3, c -1, the vector for the total dipole moment p for the configuration In addition to the two point charges, we now have an infinite grounded conductor placed in...
Flag question a) Two point charges of 40 C each, located in the x-y plane at...
Flag question a) Two point charges of 40 C each, located in the x-y plane at (1,1,0) and (-1,-1,0) respectively. to = 8.85 x 10-12 F/m. V = 4RER i) Sketch this configuration in Cartesian coordinates 12 marks] (8 marks] ii) Determine the electric field at a point 3 m on the z-axis. Q [17 marks) iii) Find the electric potential at any point Palong the x-axis. (5 marks] iv) Evaluate Vat x = 1. [2 marks] b) A thin...
Two point charges are placed on the x axis. (Figure 1) The first charge, q1 =...
Two point charges are placed on the x axis. (Figure 1) The first charge, q1 = 8.00 nC , is placed a distance 16.0 m from the origin along the positive x axis; the second charge, q2 = 6.00 nC , is placed a distance 9.00 m from the origin along the negative x axis. Part A Calculate the electric field at point A, located at coordinates (0 m, 12.0 m ).
The following diagram shows 3 point charges and their coordinates on a cartesian grid. 1. What is the net electric...
The following diagram shows 3 point charges and their coordinates on a cartesian grid. 1. What is the net electric field at P created by the other three charges? 2. For the net electric field to be zero at P, what coordinates would a -5.0q charge need to be placed? (3 m, 2 m) Q3 +1.00 (0 m,2 m) 01 +2.00 (0 m ,0 m) Q2 -3.09 (3 m ,0 m)
Two charges are located in the x–y plane. If q1 = -2.90 nC and is located...
Two charges are located in the
x–y plane. If q1 = -2.90 nC and is located at x = 0.00 m, y = 1.000
m and the second charge has magnitude of q2 = 3.40 nC and is
located at x = 1.40 m, y = 0.600 m, calculate the x and y
components, Ex and Ey, of the electric field, , in component form
at the origin, (0,0). The Coulomb Force constant is 1/(4π ε0) =
8.99 × 109...
You have four point charges. Their location and charges in Cartesian coordinates are: a positive charge, 2q, located at (a,0,0), another charge -2q located at (-a,0,0), a 3rd charge -q located at (0,0,b), and finally a fourth charge +5q located at (0,0,-b) (a) What is the total charge, and dipole moment, of this distribution of charges? Use the methods of "the multipole expansion" (Griffiths section 3.4.1) to find a simple approximate formula for V(r,0) (in spherical coordinates!) valid at points...
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...
Problem 8: Superposition of electric fields from several charges A charge Q is located at cartesian coordinates (a,a). A charge Q is located at coordinates (a, -a) A charge is located at coordinates (-a, -a). Calculate the resultant electric field (E-field) at (a, Specify the magnitude and the direction of the electric field at (a, a) -a
The following diagram shows 3 point charges and their coordinates on a cartesian grid For the net electric field to be zero at P, what coordinates would a -5.0q charge need to be placed? P (3 m, 2 m) Q3 +1.0q (0 m ,2 m) Q1 Q2 +2.0q (0 m ,0 m -3.0q (3 m,0 m
We observe two point charges in the yz-plane: one of them has charge 2q and is located in (x,y,z)-(0,0,a) and the other has a charge of -3q and is located in (x,y,z)-(0,b,a) a) Calculate the dipole moment p, and p, for the two charges around (0,0,0), and sketch for a-2, b-3, c -1, the vector for the total dipole moment p for the configuration In addition to the two point charges, we now have an infinite grounded conductor placed in...
Flag question a) Two point charges of 40 C each, located in the x-y plane at (1,1,0) and (-1,-1,0) respectively. to = 8.85 x 10-12 F/m. V = 4RER i) Sketch this configuration in Cartesian coordinates 12 marks] (8 marks] ii) Determine the electric field at a point 3 m on the z-axis. Q [17 marks) iii) Find the electric potential at any point Palong the x-axis. (5 marks] iv) Evaluate Vat x = 1. [2 marks] b) A thin...
The following diagram shows 3 point charges and their coordinates on a cartesian grid. 1. What is the net electric field at P created by the other three charges? 2. For the net electric field to be zero at P, what coordinates would a -5.0q charge need to be placed? (3 m, 2 m) Q3 +1.00 (0 m,2 m) 01 +2.00 (0 m ,0 m) Q2 -3.09 (3 m ,0 m)
Two charges are located in the
x–y plane. If q1 = -2.90 nC and is located at x = 0.00 m, y = 1.000
m and the second charge has magnitude of q2 = 3.40 nC and is
located at x = 1.40 m, y = 0.600 m, calculate the x and y
components, Ex and Ey, of the electric field, , in component form
at the origin, (0,0). The Coulomb Force constant is 1/(4π ε0) =
8.99 × 109...
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