Ampere's law provides us an easy way to calculate the magnetic field due to a symmetrical distribution of current. Its mathemfield expression is `ointvecB.dl=mu_0I_("in")`.
The quantity on the left hand side is known as line as integral of magnetic field over a closed Ampere's loop.
Only the current inside the Amperian loop contributes in

Options

A. finding magnetic field at any point on the Ampere's loop
B. line integral of magnetic field
C. in both of the above
D. in neither of them

Explanation

To solve the question regarding Ampere's Law and the contributions of current to the magnetic field, we will analyze each option provided in the context of the law itself.

### Step-by-Step Solution:

1. **Understanding Ampere's Law**:
Ampere's Law states that the line integral of the magnetic field \( \vec{B} \) around a closed loop (Ampere's loop) is equal to \( \mu_0 \) times the total current \( I_{\text{in}} \) that passes through the surface enclosed by the loop. Mathematically, it is expressed as:
\[ \oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{in}} \]

2. **Analyzing the Options**:
- **Option A**: "Finding magnetic field at any point on the Ampere loop."
- This option suggests that only the current inside the loop contributes to the magnetic field at any point on the loop. However, while the current inside the loop does contribute to the magnetic field, currents outside the loop can also influence the field at points on the loop, but they do not contribute to the integral. Therefore, this option is **incorrect**.

- **Option B**: "Line integral of the magnetic field."
- This option refers to the expression \( \oint \vec{B} \cdot d\vec{l} \), which is indeed the line integral of the magnetic field around the closed loop. This is a correct statement as it directly reflects the mathematical formulation of Ampere's Law. Thus, this option is **correct**.

- **Option C**: "Both of the above."
- Since Option A is incorrect, this option cannot be correct either. Therefore, this option is **incorrect**.

- **Option D**: "Neither of them."
- Since we have established that Option B is correct, this option is also **incorrect**.

3. **Conclusion**:
The correct answer to the question is **Option B**, which accurately describes the line integral of the magnetic field as per Ampere's Law.