The percentage increase in magnetic field B when the space within a current carrying toroid is filled with aluminum `(chi=2.1xx10^(-5))` is

Options

A. 0.002
B. `2xx10^(-3)%`
C. `2xx10^(-2)%`
D. `2xx10^(-4)%`

Explanation

To find the percentage increase in the magnetic field \( B \) when the space within a current-carrying toroid is filled with aluminum, we can follow these steps:

### Step 1: Understand the relationship between magnetic field \( B \) and susceptibility \( \chi \)
The magnetic field \( B \) in a material can be expressed in terms of the magnetic field in vacuum \( B_0 \) and the susceptibility \( \chi \) of the material:
\[ B = B_0 (1 + \chi) \]

### Step 2: Rearrange the equation to find the increase in magnetic field
From the equation above, we can express the increase in magnetic field \( B - B_0 \):
\[ B - B_0 = B_0 \chi \]

### Step 3: Express the percentage increase in magnetic field
The percentage increase in the magnetic field can be expressed as:
\[ \frac{B - B_0}{B_0} \times 100 = \chi \times 100 \]

### Step 4: Substitute the given value of susceptibility \( \chi \)
We are given that \( \chi = 2.1 \times 10^{-5} \). Substituting this value into the percentage increase formula:
\[ \text{Percentage Increase} = 2.1 \times 10^{-5} \times 100 \]

### Step 5: Calculate the percentage increase
Now, we calculate the percentage increase:
\[ \text{Percentage Increase} = 2.1 \times 10^{-3} \% \]

### Final Answer
Thus, the percentage increase in the magnetic field \( B \) when the space within a current-carrying toroid is filled with aluminum is:
\[ \text{Percentage Increase} = 0.21\% \]

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