Electric field in cartesian coordinates

In summary, the problem involves finding the electric field at a point on the x axis using the given electric potential formula in spherical polar coordinates. The coordinates are converted to Cartesian coordinates and the partial derivatives are used to calculate the electric field components.
  • #1
leventa2
7
0
[SOLVED] Electric field in cartesian coordinates

Homework Statement



Suppose the electric potential is
V(r) = C1 /r + C2 cosθ /r^2
where (r, θ, φ) are the spherical polar coordinates for points in three dimensions.
[Data: C1 = 4.3 Vm ; C2 = 1.6 Vm^2 ]
(A) Determine the electric field at a point on the x axis, E(x,0,0) where x=0.3 m. Give the three Cartesian components of the field, (Ex,Ey,Ez).

Homework Equations



r=sqrt{x^2+y^2+z^2}
θ=arccos(z/r)
E=-dV/dr

The Attempt at a Solution



cos(θ) is zero since the z coordinate is zero, and cos(θ) is z/r. I find the derivative of 4.3/r at r = 0.3, and multiply it by -1 to get 47.778 V/m. I believe that the other coordinates would be zero, since the radius for both of them is zero. However, i don't get the right answer. What would the problem be?
 
Last edited:
Physics news on Phys.org
  • #2
well i got it sub sqrt(x^2+y^2+z^2) for r and z/r for cos(theta) find all three partial derivatives and plug in values
 

FAQ: Electric field in cartesian coordinates

What is an electric field in cartesian coordinates?

An electric field in cartesian coordinates is a vector field that represents the force exerted on a charged particle at a specific point in space. It is defined as the force per unit charge at that point.

How is the electric field in cartesian coordinates calculated?

The electric field in cartesian coordinates is calculated by using the formula E = F/q, where E is the electric field, F is the force exerted on the charged particle, and q is the charge of the particle. This calculation takes into account the distance and direction of the force.

What are the units of electric field in cartesian coordinates?

The units of electric field in cartesian coordinates are newtons per coulomb (N/C). This unit describes the force per unit charge at a specific point in space.

How does the direction of the electric field in cartesian coordinates relate to the force on a charged particle?

The direction of the electric field in cartesian coordinates is the same as the direction of the force on a positively charged particle. For a negatively charged particle, the direction of the electric field is opposite to the direction of the force.

How does the electric field in cartesian coordinates vary with distance from a charged particle?

The electric field in cartesian coordinates follows an inverse-square law, meaning that it decreases in strength as the distance from the charged particle increases. This means that the electric field is strongest closest to the charged particle and becomes weaker as the distance increases.

Back
Top