Toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire wound. If the current in the wire is 11A, what is the magnetic field (a) outside the toroid, (b) inside the core of the toroid, and (c) in the empty space surrounded by the torroid.

Options

A. `(0, 0, 3 xx 10^(-2) T) `
B. `(0, 0 , 0)`
C. `(0,3 xx 10^(-2) T , 0) `
D. `(3 xx 10^(-2) T, 0,3 xx 10^(-2) T)`

Explanation

To solve the problem regarding the magnetic field in a toroid, we will follow these steps:

### Given Data:
- Inner radius of the toroid, \( r_1 = 25 \, \text{cm} = 0.25 \, \text{m} \)
- Outer radius of the toroid, \( r_2 = 26 \, \text{cm} = 0.26 \, \text{m} \)
- Total number of turns, \( N = 3500 \)
- Current flowing through the wire, \( I = 11 \, \text{A} \)

### Step 1: Magnetic Field Outside the Toroid
To find the magnetic field outside the toroid, we can use Ampere's Circuital Law, which states:
\[ \oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{\text{enclosed}} \]
For a point outside the toroid, the enclosed current \( I_{\text{enclosed}} \) is zero because the current that leaves the toroid also returns to it. Therefore:
\[ I_{\text{enclosed}} = 0 \]
Thus, the magnetic field \( B \) outside the toroid is:
\[ B_{\text{outside}} = 0 \, \text{T} \]

### Step 2: Magnetic Field Inside the Core of the Toroid
For the magnetic field inside the core of the toroid, we again apply Ampere's Circuital Law. We consider a circular path of radius \( r \) (where \( r_1 < r < r_2 \)):
\[ \oint \mathbf{B} \cdot d\mathbf{l} = B \cdot 2\pi r \]
The enclosed current \( I_{\text{enclosed}} \) for the toroid is given by:
\[ I_{\text{enclosed}} = N \cdot I = 3500 \cdot 11 \, \text{A} \]
Substituting into Ampere's Law:
\[ B \cdot 2\pi r = \mu_0 (N \cdot I) \]
Solving for \( B \):
\[ B = \frac{\mu_0 N I}{2\pi r} \]
Where \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \).

### Step 3: Magnetic Field in the Empty Space Surrounded by the Toroid
Similar to the case of the outside magnetic field, the empty space surrounded by the toroid also experiences no net current flow. Thus, the enclosed current is again zero:
\[ I_{\text{enclosed}} = 0 \]
Therefore, the magnetic field in the empty space surrounded by the toroid is:
\[ B_{\text{surrounded}} = 0 \, \text{T} \]

### Summary of Results:
(a) Magnetic field outside the toroid: \( B_{\text{outside}} = 0 \, \text{T} \)

(b) Magnetic field inside the core of the toroid:
\[ B = \frac{\mu_0 N I}{2\pi r} \]
Substituting values for \( r \) (between \( r_1 \) and \( r_2 \)) will give the specific magnetic field strength.

(c) Magnetic field in the empty space surrounded by the toroid: \( B_{\text{surrounded}} = 0 \, \text{T} \)