Magnetic field induction at any point outside a toroid is ……………… .

Answer

To determine the magnetic field induction at any point outside a toroid, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Configuration**:
- A toroid is a doughnut-shaped coil of wire, and we need to analyze the magnetic field outside this toroidal structure when current flows through it.

2. **Use Ampere's Circuital Law**:
- Ampere's Circuital 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 \( I \) enclosed by that loop:
\[ \oint B \cdot dl = \mu_0 I_{\text{enclosed}} \]

3. **Choose an Imaginary Loop**:
- To apply Ampere's Law, we can consider an imaginary circular loop that lies outside the toroid. This loop will help us analyze the magnetic field at points outside the toroid.

4. **Determine the Enclosed Current**:
- For a point outside the toroid, the current enclosed by our imaginary loop is zero. This is because the current flowing through the toroid does not pass through the area enclosed by our loop.

5. **Apply Ampere's Law**:
- Since the enclosed current \( I_{\text{enclosed}} = 0 \), we can substitute this into Ampere's Law:
\[ \oint B \cdot dl = \mu_0 \cdot 0 = 0 \]

6. **Conclude the Magnetic Field**:
- From the above equation, we conclude that the line integral of the magnetic field \( B \) around our loop is zero. This implies that the magnetic field \( B \) at any point outside the toroid is also zero:
\[ B = 0 \quad \text{(outside the toroid)} \]

### Final Answer:
The magnetic field induction at any point outside a toroid is **zero**.

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