Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately

Options

A. spheres
B. planes
C. paraboloids
D. ellipsoids

Answer

To solve the question regarding the equipotential surfaces at a great distance from a collection of charges whose total sum is not zero, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Equipotential Surfaces**:
Equipotential surfaces are those surfaces where the electric potential is the same at every point. This means that no work is done when moving a charge along these surfaces.

2. **Considering a Collection of Charges**:
When we have a collection of charges, if the total charge is not zero, the electric field will be present at a distance from these charges. The behavior of the electric field and potential at a distance from the charges can be analyzed.

3. **Point Charge Approximation**:
At a great distance from a collection of charges, we can approximate the entire collection as a single point charge. This is due to the fact that the electric field decreases with the square of the distance from the charge.

4. **Electric Potential Due to a Point Charge**:
The electric potential \( V \) at a distance \( r \) from a point charge \( Q \) is given by the formula:
\[ V = \frac{kQ}{r} \]
where \( k \) is Coulomb's constant. As \( r \) increases, the potential \( V \) decreases.

5. **Equipotential Surfaces at a Distance**:
At a distance \( r \) from the charge, the potential remains constant for all points that are equidistant from the charge. Thus, the equipotential surfaces around a point charge are spherical surfaces centered around the charge.

6. **Conclusion**:
Therefore, at a great distance from a collection of charges whose total sum is not zero, the equipotential surfaces can be approximated as spherical surfaces. This means that the correct answer to the question is that the equipotential surfaces are approximately spherical.

### Final Answer:
The equipotential surfaces at a great distance from a collection of charges whose total sum is not zero are approximately spherical.