An electric diple is put in north-south direction in a sphere filled with water. Which statement is correct:

Options

A. electric flux is coming towards sphere
B. electric flux is coming out of sphere
C. electric flux entering into sphere and leaving the sphere are same
D. water does not permit electric flux to enter into sphere

Answer

To solve the problem of determining which statement is correct regarding an electric dipole placed in a north-south direction inside a sphere filled with water, we can follow these steps:

### Step 1: Understand the Electric Dipole
An electric dipole consists of two equal and opposite charges, +q and -q, separated by a distance 'd'. In this case, the dipole is oriented in the north-south direction.

### Step 2: Analyze the Electric Flux
The electric flux (Φ) through a closed surface is given by Gauss's law:
\[ Φ = \frac{Q_{enc}}{\epsilon_0} \]
where \(Q_{enc}\) is the total charge enclosed by the surface and \(\epsilon_0\) is the permittivity of free space.

### Step 3: Calculate the Enclosed Charge
For an electric dipole, the total charge enclosed within any closed surface that contains both charges is zero:
\[ Q_{enc} = +q + (-q) = 0 \]
Thus, the electric flux through the sphere is:
\[ Φ = \frac{0}{\epsilon_0} = 0 \]

### Step 4: Interpret the Results
Since the total electric flux is zero, this implies that the electric flux entering the sphere is equal to the electric flux leaving the sphere. Therefore, we can conclude:
- The electric flux entering the sphere and the electric flux leaving the sphere are the same.

### Step 5: Evaluate the Statements
1. Electric flux is coming towards the sphere: **False** (Total flux is zero)
2. Electric flux is coming out of the sphere: **False** (Total flux is zero)
3. Electric flux entering the sphere and leaving the sphere are the same: **True** (This is correct)
4. Water does not permit electric flux: **False** (Water is a dielectric and permits electric flux)

### Conclusion
The correct statement is that the electric flux entering the sphere and leaving the sphere are the same.

---