# Electric Fields and Electric Potential

Four quick conceptual questions:

1) Is the electric field (E = -delta V / delta s) always a positive number (or zero)? That is, is it always the absolute value of the magnitude of the electric field? Or can it have a negative value?

2) Is electric potential (delta V) always negative? The answer to one of the questions in my book says: 'the negative value of delta V in this question simply indicates that the electric potential of the negative plate is less than that of the positive plate.' This seems to imply that electric potential is always negative.

3) My book gives this equation for electric potential energy:

delta U =(q)(delta V)=(q)(E)(d)

but if delta V = (-E)(delta s),

shouldn't delta U = (q)(-E)(d)?

4) Also, can you give a quick explanation of what exactly electric potential is, and how it relates to electric potential energy?

Thank you!

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#### Solution Preview

1) Electric field is a vector quantity, i.e., it has a direction and some magnitude. The magnitude of any vector quantity will always be positive.

Any vector vec(A) can be written as:

vec(A) = A*unit_vec(A)

where A = magnitude of vector vec(A)

and, unit_vec(A) = unit vector along vector vec(A).

Now, E = -dV/ds represents a vector quantity, containing the information of magnitude and direction. So, if the direction is opposite to our ...

#### Solution Summary

The solution carefully explains each of the four conceptual questions posed in the subject of electric fields and potentials, drawing on relevant equations to give a fuller understanding.