Mark the correct statement

Options

A. A solid conducting sphere holds more charge than a hallow conducting sphere of the same radius
B. Two equipotential surface mat intersects
C. When a conductor is earthed, charge always flows from conductor to earth
D. No work is done in taking a possitive charge from one point to another point inside a negetively charged metallic sphere

Answer

To determine which statement is correct among the four provided, we will analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement:** A solid conducting sphere holds more charge than a hollow conducting sphere of the same radius.

- **Explanation:** When a charge is given to a conducting sphere, whether solid or hollow, the charge distributes itself uniformly on the outer surface. The capacity of both the solid and hollow conducting spheres to hold charge depends only on their radius and shape, which are the same in this case. Therefore, both spheres can hold the same amount of charge.
- **Conclusion:** This statement is **incorrect**.

### Step 2: Analyze the second statement
**Statement:** Two equipotential surfaces may intersect.

- **Explanation:** An equipotential surface is defined as a surface where the electric potential is the same at every point. If two equipotential surfaces were to intersect, it would imply that at the point of intersection, the electric potential would have two different values, which is not possible. Therefore, equipotential surfaces cannot intersect.
- **Conclusion:** This statement is **incorrect**.

### Step 3: Analyze the third statement
**Statement:** When a conductor is earthed, charge always flows from the conductor to the earth.

- **Explanation:** The flow of charge depends on the potential difference between the conductor and the earth. If the conductor is at a higher potential than the earth, charge will flow from the conductor to the earth. Conversely, if the conductor is at a lower potential than the earth, charge will flow from the earth to the conductor. Thus, it is not always true that charge flows from the conductor to the earth.
- **Conclusion:** This statement is **incorrect**.

### Step 4: Analyze the fourth statement
**Statement:** No work is done in taking a positive charge from one point to another point inside a negatively charged metallic sphere.

- **Explanation:** Inside a charged metallic sphere, the electric field is zero due to the distribution of charge on the surface. Since the electric field is zero, the electric potential is constant throughout the interior of the sphere. When moving a charge within this region, there is no change in electric potential, and thus no work is done. The work done is given by the formula \( W = q \Delta V \), where \( \Delta V \) is the potential difference. Since \( \Delta V = 0 \), the work done \( W = 0 \).
- **Conclusion:** This statement is **correct**.

### Final Answer
The correct statement is: **No work is done in taking a positive charge from one point to another point inside a negatively charged metallic sphere.**

---