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.

Explanation

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

### Step 1: Understand Equipotential Surfaces
Equipotential surfaces are surfaces where the electric potential is the same at every point. For a point charge, these surfaces are spherical in shape.

**Hint:** Recall that equipotential surfaces are defined by the condition that the electric potential is constant across the surface.

### Step 2: Consider a Point Charge
For a single point charge \( q \), the equipotential surfaces are concentric spheres centered around the charge. The potential \( V \) at a distance \( r \) from the charge is given by the formula:
\[ V = \frac{kq}{r} \]
where \( k \) is Coulomb's constant.

**Hint:** Remember that the potential decreases with distance from the charge, leading to spherical equipotential surfaces.

### Step 3: Analyze a Collection of Charges
Now, consider a collection of charges where the total charge \( Q \) is not equal to zero. At a great distance from this collection, the behavior of the electric field and potential can be approximated as if it were a single point charge with charge \( Q \).

**Hint:** Think about how the superposition principle applies to electric fields from multiple charges.

### Step 4: Determine the Effective Charge
At a large distance, the entire collection of charges can be treated as a single point charge with the total charge \( Q \). Thus, the potential at a distance \( r \) from this collection can be expressed similarly to that of a point charge:
\[ V = \frac{kQ}{r} \]

**Hint:** Consider how the total charge influences the potential at large distances.

### Step 5: Conclude the Shape of Equipotential Surfaces
Since the potential behaves like that of a point charge at a large distance, the equipotential surfaces for this collection of charges will also be spherical. Therefore, at a great distance from the collection of charges, the equipotential surfaces are approximately spherical.

**Hint:** Relate the concept of distance and charge distribution to the resulting shape of the equipotential surfaces.

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