Electrostatics - Coulomb's Law

AI Thread Summary
The discussion centers on understanding the origin of the cos(theta) term in the formula for dE from Griffith's Electrodynamics. It is clarified that when adding the r_hat vectors, the result simplifies to 2(z/r)z_hat, where z/r is equivalent to cos(theta). Participants express concern about the complexity of deriving this formula independently. However, it is emphasized that the formula is provided in a general form, alleviating the need for self-derivation. The conversation highlights the importance of grasping the underlying concepts in electrostatics.
jinksys
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I'm doing example 2.1 in Griffith's Electrodynamics book. Can someone explain where the cos(theta) comes from in the formula for dE? The formula is on the first image: Here.
 
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SOLVED:

I see what's going on. If you add the r_hat vectors you end up with 2(z/r)z_hat. z/r=cos(theta). So we end up with 2cos(theta)z_hat.
 
that looks so hard. are you supposed to figure out that formula all by yourself
 
bael said:
that looks so hard. are you supposed to figure out that formula all by yourself

No, the formula is given to you in a general form.
 

Thread 'How to picture the vector potential?'

Susskind (in The Theoretical Minimum, volume 1, pages 203-205) writes the Lagrangian for the magnetic field as ##L=\frac m 2(\dot x^2+\dot y^2 + \dot z^2)+ \frac e c (\dot x A_x +\dot y A_y +\dot z A_z)## and then calculates ##\dot p_x =ma_x + \frac e c \frac d {dt} A_x=ma_x + \frac e c(\frac {\partial A_x} {\partial x}\dot x + \frac {\partial A_x} {\partial y}\dot y + \frac {\partial A_x} {\partial z}\dot z)##. I have problems with the last step. I might have written ##\frac {dA_x} {dt}...
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Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (Second part)'

Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (Second part)'

I am reading the Griffith, Electrodynamics book, 4th edition, Example 4.8. I want to understand some issues more correctly. It's a little bit difficult to understand now. > Example 4.8. Suppose the entire region below the plane ##z=0## in Fig. 4.28 is filled with uniform linear dielectric material of susceptibility ##\chi_e##. Calculate the force on a point charge ##q## situated a distance ##d## above the origin. In the page 196, in the first paragraph, the author argues as follows ...
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