Suppose the electric potential is V(r) = C1/r + C2 cos?/r^2 where (r, ?, f) are

Question

Suppose the electric potential is
V(r) = C1/r + C2 cos?/r^2
where (r, ?, f) are the spherical polar coordinates for points in three dimensions.
[Data: C1 = 3.5 Vm ; C2 = 1.0 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).
Ex=? Ey=? Ez=?
(B) Determine the electric field at a point on the z axis, E(0,0,z) where z = 0.3 m. Give the three Cartesian components of the field, (Ex,Ey,Ez).
Ex=? Ey=? Ez=?

Explanation / Answer

Remember that the standard unit for an electric field is Volts/meter (V/m). In one dimension (usually x-axis), the electric field is defined by: E = dV/dx , where E is the electric field and dV/dx is the partial derivative with respect to x. Since you are given V, you must take the derivative of your V(r) function to find E. Since you are dealing with more than one variable, take the partial derivatives of all three variables.

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