In using Ampere's law,to find the magnetic field inside a straight long soleniod the loop that is taken is

Options

A. A circular loop in a with the soleniod
B. a rectangular loop in a plane is perpendicular to the axis of the solenoid
C. A rectangulr loop in a plane containing the axis of the solenoid the loop being totally within the soleniod
D. A rectangular loop in a plane containing the axis of the soleniod the loop being partly inside and partly outside it

Answer

To solve the question regarding the application of Ampere's law to find the magnetic field inside a straight long solenoid, we will analyze the options provided and determine which loop is appropriate for our calculations.

### Step-by-Step Solution:

1. **Understanding Ampere's Law**:
Ampere's law states that the line integral of the magnetic field \( B \) around a closed loop is equal to the permeability of free space \( \mu_0 \) times the total current \( I \) passing through the loop. Mathematically, it is expressed as:
\[ \oint B \cdot dl = \mu_0 I_{enc} \]

2. **Analyzing the Options**:
We have four options regarding the type of loop we can use to apply Ampere's law in the context of a solenoid.

- **Option A**: A circular loop with the solenoid.
- **Option B**: A rectangular loop in a plane perpendicular to the axis of the solenoid.
- **Option C**: A rectangular loop in a plane containing the axis of the solenoid, the loop being totally within the solenoid.
- **Option D**: A rectangular loop in a plane containing the axis of the solenoid, the loop being partially inside and partially outside.

3. **Evaluating Each Option**:
- **Option A**: A circular loop is not suitable because it does not align well with the uniform magnetic field inside the solenoid.
- **Option B**: A rectangular loop perpendicular to the axis of the solenoid results in \( B \cdot dl = 0 \) since the angle \( \theta \) between \( B \) and \( dl \) is 90 degrees, leading to no contribution to the integral.
- **Option C**: A rectangular loop totally within the solenoid would not allow us to measure the current effectively since the magnetic field lines are uniform and parallel to the axis of the solenoid.
- **Option D**: A rectangular loop that is partially inside and partially outside the solenoid allows us to utilize Ampere's law effectively. The segment of the loop inside the solenoid will experience the magnetic field, while the segments outside will not contribute to the integral.

4. **Conclusion**:
The best choice for applying Ampere's law to find the magnetic field inside a straight long solenoid is **Option D**: a rectangular loop in a plane containing the axis of the solenoid, the loop being partially inside and partially outside.

### Final Answer:
**Option D**: A rectangular loop in a plane containing the axis of the solenoid, the loop being partially inside and partially outside.