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According to Ampère's circuital law, the...

According to Ampère's circuital law, the circulation of magnetic field in a closed curve is equal to ........ Times the total current enclosed within the closed curve.

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To answer the question regarding Ampère's circuital law, we need to understand the relationship it describes between the magnetic field and the current flowing through a closed loop. ### Step-by-Step Solution: 1. **Understanding Ampère's Circuital Law**: Ampère's circuital law states that the circulation of the magnetic field (B) around a closed loop is proportional to the total current (I) enclosed by that loop. Mathematically, it can be expressed as: \[ \oint \mathbf{B} \cdot d\mathbf{L} = \mu_0 I_{\text{enclosed}} \] where \(\oint \mathbf{B} \cdot d\mathbf{L}\) is the line integral of the magnetic field around the closed loop, \(\mu_0\) is the permeability of free space, and \(I_{\text{enclosed}}\) is the total current passing through the loop. 2. **Identifying the Proportionality Constant**: From the equation, we can see that the circulation of the magnetic field is equal to \(\mu_0\) times the total current enclosed. Therefore, the answer to the question is: \[ \text{the circulation of magnetic field in a closed curve is equal to } \mu_0 \text{ times the total current enclosed.} \] 3. **Conclusion**: Thus, according to Ampère's circuital law, the circulation of the magnetic field in a closed curve is equal to \(\mu_0\) times the total current enclosed within that closed curve. ### Final Answer: The circulation of the magnetic field in a closed curve is equal to **\(\mu_0\)** times the total current enclosed within the closed curve. ---
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