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[SOLVED] Electric field in cartesian coordinates
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).
r=sqrt{x^2+y^2+z^2}
θ=arccos(z/r)
E=-dV/dr
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?
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?
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