Problem 1. Electric field of an electric dipole An “electric dipole" is an arrangement of (typically) two charges that have equal magnitude and opposite sign. Suppose a charge -q is located on the z axis at z = -d/2 and a charge +q is located also on the z axis at z = :+d/2. Note that there is a factor of two in the positions relative to the example worked in the notes for the symmetric charges. The reason for this difference will be explained in problem 2. For simplicity, we will calculate the field in the x – z plane – i.e. for y = 0 – and then use the cylindrical symmetry to generalize the result. a. Calculate Ē(0,0, 0). b. Calculate the complete electric field for a = 0. In other words obtain Ē(0,0, z). You may express your results using absolute values in the denominator but then show the expressions with the correct signs in the regions z < -d/2, –d/2 < z < d/2, z > d/2. c. Calculate the complete electric field for z = 0. In other words obtain Ē (x,0,0).
Problem 1. Electric field of an electric dipole An “electric dipole" is an arrangement of (typically) two charges that have equal magnitude and opposite sign. Suppose a charge -q is located on the z axis at z = -d/2 and a charge +q is located also on the z axis at z = :+d/2. Note that there is a factor of two in the positions relative to the example worked in the notes for the symmetric charges. The reason for this difference will be explained in problem 2. For simplicity, we will calculate the field in the x – z plane – i.e. for y = 0 – and then use the cylindrical symmetry to generalize the result. a. Calculate Ē(0,0, 0). b. Calculate the complete electric field for a = 0. In other words obtain Ē(0,0, z). You may express your results using absolute values in the denominator but then show the expressions with the correct signs in the regions z < -d/2, –d/2 < z < d/2, z > d/2. c. Calculate the complete electric field for z = 0. In other words obtain Ē (x,0,0).
Related questions
Question
Transcribed Image Text:Problem 1. Electric field of an electric dipole
An “electric dipole" is an arrangement of (typically) two charges that have equal magnitude and opposite
sign. Suppose a charge -q is located on the z axis at z =
-d/2 and a charge +q is located also on the z
+d/2. Note that there is a factor of two in the positions relative to the example worked in the
axis at z
notes for the symmetric charges. The reason for this difference will be explained in problem 2. For
simplicity, we will calculate the field in the x
symmetry to generalize the result.
z plane – i.e. for y = 0 – and then use the cylindrical
%3D
a. Calculate E(0, 0, 0).
b. Calculate the complete electric field for x = 0. In other words obtain E(0, 0, z). You may express
your results using absolute values in the denominator but then show the expressions with the
correct signs in the regions z < -d/2, -d/2 < z < d/2, z > d/2.
c. Calculate the complete electric field for z = 0. In other words obtain E(x, 0,0).
d. Calculate the complete electric field for all z and x values, Ē(x, 0, z)
e. Generalize your result from part d by making the replacement i → î1, x → r1 .
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps
