Which of the following statements is valid:.A) If the potential throughtout a particular region is constant, the field throughout the region must be zero. B) If the field throughout a particular region is constant, the potential throughout that region must be zero. C) If the field at a particular point is zero, the potential at that point must be zero. D) If the potential at a particular point is zero, the field at that point must be zero.

Option A is the only valid statement.

Explanation:

A)The electric field intensity is defined by the relationship:

E= -ΔV/Δr.

Now, according to the relationship above, the electric field would be the negative gradient of electric potential. Now, if the electric potential is constant throughout the given region of space, then the change in electric potential would be ΔV=0.

Thu,E= 0.

So the answer is that, E will be zero in this case.

So, the statement is valid.

B) Statement not valid because the field is the gradient of the potential. Hence, the field would be zero in any region where the potential is constant. However, constant does not necessarily mean a value of zero. With that being said, we can always change the definition of the potential function by adding a constant, to thus make it zero there. But then the potential will no longer be zero at infinity or in any different “flat” regions.

C) Statement not valid because, for the fact that electric field is zero at a particular point, it doesn't necessarily

imply that the electric potential is zero at that point. A good example would be the case of two identical charges which are separated by some distance. At the midpoint between the charges, the

electric field due to the charges would be zero. However, the electric potential due to the charges at that same point would not be zero. Thus, the potential will either have two positive contributions, if the charges are positive, or two negative contributions, if the charges are negative.

(D) Statement is not valid because, for the fact that electric potential is zero at a particular point, it does not necessarily imply that the electric field is zero at that point. A good example would be the case of a dipole, which

has two charges of the same magnitude, but opposite sign, and are separated by some distance. At

the midpoint between the charges, the electric potential due to the charges would be zero, but the electric field due to the charges at that same point would not be zero.

15.3 cos 65 degrees trig