In toroid magnetic field magnetic field on axis will be radius = 0.5 cm, current = 1.5 A, turns = 250, permeability = 700

Options

A. 7.5 Tesla
B. 10.5 Tesla
C. 4.5 Tesla
D. 15.5 Tesla

Explanation

To solve the problem of finding the magnetic field at the axis of a toroid, we will use the formula for the magnetic field in a toroid. Here are the steps to arrive at the solution:

### Step 1: Write down the formula for the magnetic field in a toroid
The magnetic field \( B \) at the axis of a toroid is given by the formula:

\[ B = \frac{\mu_0 \mu_r N I}{2 \pi r} \]

where:
- \( \mu_0 \) is the permeability of free space (\( 4\pi \times 10^{-7} \, \text{T m/A} \)),
- \( \mu_r \) is the relative permeability,
- \( N \) is the number of turns,
- \( I \) is the current,
- \( r \) is the radius.

### Step 2: Substitute the known values into the formula
Given:
- \( \mu_r = 700 \)
- \( N = 250 \)
- \( I = 1.5 \, \text{A} \)
- \( r = 0.5 \, \text{cm} = 0.5 \times 10^{-2} \, \text{m} \)

Now substituting these values into the formula:

\[ B = \frac{(4\pi \times 10^{-7}) \times 700 \times 250 \times 1.5}{2 \pi \times (0.5 \times 10^{-2})} \]

### Step 3: Simplify the equation
We can simplify the equation by canceling \( \pi \):

\[ B = \frac{(4 \times 700 \times 250 \times 1.5) \times 10^{-7}}{2 \times (0.5 \times 10^{-2})} \]

### Step 4: Calculate the numerator and denominator
Calculating the numerator:

\[ 4 \times 700 = 2800 \]
\[ 2800 \times 250 = 700000 \]
\[ 700000 \times 1.5 = 1050000 \]

Calculating the denominator:

\[ 2 \times (0.5 \times 10^{-2}) = 1 \times 10^{-2} = 0.01 \]

### Step 5: Final calculation
Now substituting back into the equation:

\[ B = \frac{1050000 \times 10^{-7}}{0.01} \]
\[ B = 1050000 \times 10^{-5} = 10.5 \, \text{T} \]

### Conclusion
Thus, the magnetic field at the axis of the toroid is:

\[ B = 10.5 \, \text{T} \]

### Answer
The answer is \( \text{Option B: } 10.5 \, \text{T} \).

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