Angle of dip at a place is `30^(@)` . If the vertical component of earth's magnetic field at that point is `7.5 xx 10^(-5)` T, then the total magnetic field of earth at the point will be .

Options

A. `7.5 xx 10^(-5) T `
B. `1.5 xx 10^(-4) T`
C. `8.67 xx 10^(-5) T`
D. `1.5 xx 10^(-5) T `

Explanation

To find the total magnetic field of the Earth at a point where the angle of dip is given as \(30^\circ\) and the vertical component of the Earth's magnetic field is \(7.5 \times 10^{-5}\) T, we can follow these steps:

### Step 1: Understand the relationship between components of the magnetic field
The total magnetic field \(B\) can be related to its vertical component \(B_v\) and horizontal component \(B_h\) using the angle of dip \(\delta\):
\[ B_v = B \sin(\delta) \]
\[ B_h = B \cos(\delta) \]

### Step 2: Use the given vertical component and angle of dip
We know:
- \(B_v = 7.5 \times 10^{-5}\) T
- \(\delta = 30^\circ\)

Using the sine of the angle of dip:
\[ B_v = B \sin(30^\circ) \]
Since \(\sin(30^\circ) = \frac{1}{2}\), we can substitute this into the equation:
\[ 7.5 \times 10^{-5} = B \times \frac{1}{2} \]

### Step 3: Solve for the total magnetic field \(B\)
To isolate \(B\), multiply both sides by 2:
\[ B = 2 \times 7.5 \times 10^{-5} \]
\[ B = 15 \times 10^{-5} \text{ T} \]
\[ B = 1.5 \times 10^{-4} \text{ T} \]

### Final Answer
The total magnetic field of the Earth at that point is:
\[ B = 1.5 \times 10^{-4} \text{ T} \]

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