Electrostatics - Coulomb's Law

[jinksys]

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.

 

[jinksys]

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.

 

[bael]

that looks so hard. are you supposed to figure out that formula all by yourself

 

[jinksys]

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.

 

[sardar]

Coulomb's Law is a fundamental principle in electrostatics that describes the force between two charged particles. It states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

In the given formula for dE, the cos(theta) term represents the angle between the direction of the electric field and the direction of the displacement vector. This angle is important because it affects the magnitude of the electric field experienced by the charged particle. When the displacement vector and the electric field are parallel, the cosine of the angle is equal to 1, resulting in a larger value for dE. However, when the displacement vector and the electric field are perpendicular, the cosine of the angle is equal to 0, resulting in a smaller value for dE.

In example 2.1 of Griffith's Electrodynamics book, the angle theta is introduced in order to calculate the electric field at a point on the x-axis due to a charged particle located at a point off the x-axis. The angle theta is used to determine the component of the electric field in the x-direction, which is necessary for the calculation of dE.

In summary, the cos(theta) term in the formula for dE represents the effect of the angle between the electric field and the displacement vector on the magnitude of the electric field experienced by a charged particle. It is an important factor in accurately calculating the electric field using Coulomb's Law.