Consider the magnetic field produced by a finitely long current carrying wire .

Options

A. (a)The lines of field will be concentric circles with centre on the wire.
B. (b)There can be two points in the same plane where magnitude of magnetic field is same.
C. (c)There can be large number of points where magnitude of the magnetic field is same.
D. (d)The magnetic field at a point is inversely proportional to the distance of the point from the wire.

Explanation

To solve the question regarding the magnetic field produced by a finitely long current-carrying wire, we will analyze the magnetic field characteristics and evaluate the given statements.

### Step-by-Step Solution:

1. **Understanding the Magnetic Field Due to a Current-Carrying Wire**:
- When a current flows through a wire, it generates a magnetic field around it. For an infinitely long straight wire, the magnetic field lines are concentric circles centered around the wire.

**Hint**: Recall the right-hand rule to determine the direction of the magnetic field around a current-carrying wire.

2. **Formula for Magnetic Field**:
- The magnetic field (B) at a distance (r) from a long straight wire carrying a current (I) is given by the formula:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
- Here, \(\mu_0\) is the permeability of free space.

**Hint**: Remember that the magnetic field strength decreases as the distance from the wire increases.

3. **Analyzing the Statements**:
- **Statement A**: The lines of the magnetic field will be concentric circles with the center on the wire.
- This statement is **correct** because the magnetic field lines around a straight wire are indeed concentric circles.

- **Statement B**: There can be two points in the same place where the magnetic field is the same.
- This statement is also **correct**. Due to the nature of the magnetic field, multiple points can have the same magnetic field strength at different distances from the wire.

- **Statement C**: There can be a large number of points where the magnitude of the field is the same as they are long wire produced by the magnetic field.
- This statement is **correct** as well. The magnetic field strength can be the same at various points around the wire.

- **Statement D**: The magnetic field at a point is inversely proportional to the distance of the point from the wire.
- This statement is **incorrect**. The magnetic field is inversely proportional to the distance (r), but not simply to r; it is proportional to \( \frac{1}{r} \), not \( \frac{1}{r^2} \).

**Hint**: Compare the nature of the magnetic field with respect to distance and remember the specific formula.

4. **Conclusion**:
- The correct statements are A, B, and C. Statement D is incorrect because the relationship is not as stated.

### Final Answer:
- Statements A, B, and C are correct. Statement D is incorrect.