1. (10 points) Which of the following is not true of vector fields? A. Each poin

Question

1. (10 points) Which of the following is not true of vector fields? A. Each point in space has a corresponding vector B. The gradient of a scalar field produces a vector field C. The Electric field can be represented as a vector field D. The magnitude of the vector field decreases radially outward from a point charge. E. The Electric Potential field can be represented as a vector field 2. (10 points) What is the magnitude of the electric field midway between a dipole located on the X axis with a positive charge q at -and a negative charge, -q, located at 2 Express in terms of the dipole charge q, and the dipole separation distance d? B. 2 C.-2 D. 4 di di 3. (10 points) Which charge arrangement will produce the greatest magnitude (positive or negative) of electric field in the center? A. Two equal dipoles, with charges located a distance d from the origin on the X and Y axes receptively. B. Four equal positive charges located a distance d along each axis C. Four equal negative charges located a distance d along each axis D. All of the above produce an equal non-zero magnitude E. All of the above produce an equal magnitude that is exactly zero

Explanation / Answer

1)
A) True
Each position in space can be associated with a vector called position vector.

B) True.
For an example, the gradient of electric potential (scalar) is electric field, which is a vector.

C) True
Electric field is a vector, which follows all rules of vector algebra.

D) True
Since the magnitude is inversely proportional to the square of the distance, magnitude decreases.

E) False
Electric potential is a scalar.

2)
Electric field due to +q located at - d/2 is
E1 = Kq/(d/2)2 towards right
= 4 Kq/d2                  [Towards right is positive]
Electric field due to -q located at + d/2 is
E2 = 4 Kq/d2 towards right

Total electric field at the midpoint is
E = E1 + E2 = 8 Kq/d2
None of the options are correct

3)
Correct answer is option A.
Only in the case of dipole, there is non-zero electric field at the center

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