Ratio between total intensity of magnetic field at equator to poles is

Options

A. `1:1`
B. `1:2`
C. `2:1`
D. `1:4`

Answer

To find the ratio between the total intensity of the magnetic field at the equator to that at the poles, we can follow these steps:

### Step 1: Understanding the Magnetic Field Components
At any point on Earth, the magnetic field can be resolved into two components: the horizontal component (Bh) and the vertical component (Bv). The total magnetic field intensity (B) can be expressed as:
\[ B = \sqrt{B_h^2 + B_v^2} \]

### Step 2: Magnetic Field at the Equator
At the equator, the angle of dip (δ) is 0 degrees. Therefore, the horizontal and vertical components can be expressed as:
- Horizontal component (Bh) at the equator:
\[ B_h = B \cos(0^\circ) = B \]
- Vertical component (Bv) at the equator:
\[ B_v = B \sin(0^\circ) = 0 \]

Thus, the total magnetic field intensity at the equator (Be) is:
\[ B_e = \sqrt{B_h^2 + B_v^2} = \sqrt{B^2 + 0^2} = B \]

### Step 3: Magnetic Field at the Poles
At the poles, the angle of dip (δ) is 90 degrees. Therefore, the horizontal and vertical components can be expressed as:
- Horizontal component (Bh) at the poles:
\[ B_h = B \cos(90^\circ) = 0 \]
- Vertical component (Bv) at the poles:
\[ B_v = B \sin(90^\circ) = B \]

Thus, the total magnetic field intensity at the poles (Bp) is:
\[ B_p = \sqrt{B_h^2 + B_v^2} = \sqrt{0^2 + B^2} = B \]

### Step 4: Calculating the Ratio
Now, we can calculate the ratio of the total magnetic field intensity at the equator to that at the poles:
\[ \text{Ratio} = \frac{B_e}{B_p} = \frac{B}{B} = 1 \]

### Conclusion
The ratio between the total intensity of the magnetic field at the equator to that at the poles is:
\[ \text{Ratio} = 1:1 \]