If the total magnetic field strength (H) due to the earth is `28 Am^-1` then the total magnetic induction due to the earth is:

Options

A. 28 T
B. 280 grams
C. 0.352 gauss
D. 0.352 T

Explanation

To find the total magnetic induction (B) due to the Earth when the magnetic field strength (H) is given as 28 Am^-1, we can use the following steps:

### Step 1: Understand the relationship between B and H
The magnetic induction (B) is related to the magnetic field strength (H) by the equation:
\[ B = \mu H \]
where \( \mu \) is the permeability of the medium.

### Step 2: Identify the value of permeability (μ)
For free space (or air, which is a good approximation for many practical purposes), the permeability \( \mu \) is given by:
\[ \mu = 4\pi \times 10^{-7} \, \text{T m/A} \]

### Step 3: Substitute the values into the equation
Now, substituting the values of \( \mu \) and \( H \) into the equation:
\[ B = (4\pi \times 10^{-7}) \times 28 \]

### Step 4: Calculate the value of B
Calculating this gives:
\[ B = 4\pi \times 28 \times 10^{-7} \]
\[ B \approx 352 \times 10^{-7} \, \text{T} \]

### Step 5: Convert the units from Tesla to Gauss
Since 1 Tesla = \( 10^4 \) Gauss, we convert:
\[ B = 352 \times 10^{-7} \, \text{T} \times 10^4 \, \text{Gauss/T} \]
\[ B = 0.352 \, \text{Gauss} \]

### Final Answer
Thus, the total magnetic induction due to the Earth is:
\[ B \approx 0.352 \, \text{Gauss} \]

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