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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)
A point charge q1 = 10.0 nC is located at the origin and another point charge...
A point charge q1 = 10.0 nC is located at the origin and another point charge q2 = −5.0 nC is located at position (6.0, 0 cm). (a) Find the potential at (3.0 cm, 0). (b) Find the potential at (0, 3.0 cm). (c) Find the potential at (6.0 cm, 3.0 cm). (d) At what position(s) along the x-axis would the potential equal zero? (e) Sketch the electric field and equipotential lines surrounding the charges and note the approximate location(s)...
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)
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