9. Over a certain region of space, the electric potential is V = . (a) Find the expressions for the x, y, and z components of the electric field over this region. (b) What is the magnitude of the field at the point P that has coordinates (1.00, 0, 22.00) m?

a)

The expression for the electric potential in this problem is:

where

x, y, z are the three spatial coordinates

The relationship between components of the electric field and electric potential is:

Therefore, we have to calculate the derivatives of the potential over the three variables.

Doing so, we find:

b)

Here we want to find the magnitude of the electric field at the point P that has coordinates

P (1.00, 0, 22.00) m

First of all, we find the components of the electric field at that point by substituting

x = 1.00

y = 0

z = 22.0

We find:

Now, the magnitude of the electric field is given by

And by substituting,

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