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Q. 46

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 739

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Short Answer

The electric potential in a region of space is , where and are in meters. What are the strength and direction of the electric field at ? Give the direction as an angle or (specify which) from the positive -axis

The strength of the electric field is, pointing degrees below the axis (clockwise).

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Step by Step Solution

Step 1: Given information 

We have given that the electric potential in a region of space is -, where and are in meters.

We need to find that the strength and direction of the electric field at , ,

Step 2: Simplify

Considering the potential

,

At point , the potential will be

For the electric field, it is a vector quantity. As we have two dimensions, we will have to derive in the two directions; that is

Performing this derivation, we get

For the point , the electric field vector will be

The magnitude of this vector will be

,

which one could also see as a multiple of right triangle. This is to say that the magnitude of the electric field at the point as.

The direction of the electric field will be

,

which means that the vector point degrees lower than the direction of the positive axis.

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