A point near the equator has

Options

A. `B_(v)gtgtB_(H)`
B. `B_(H)gtgtB_(v)`
C. `B_(v)=B_(H)`
D. `B_(v)=B_(H)0`

Answer

To solve the problem regarding the magnetic field components at a point near the equator, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Magnetic Field Components**:
At any point on Earth, the magnetic field can be decomposed into two components: the horizontal component (BH) and the vertical component (BV).

2. **Identifying the Situation at the Equator**:
Near the equator, the magnetic field lines are nearly parallel to the surface of the Earth. This means that the vertical component of the magnetic field (BV) is very small compared to the horizontal component (BH).

3. **Setting Up the Relationship**:
We can express the relationship between the vertical and horizontal components using the tangent function:
\[ \tan(\theta) = \frac{BV}{BH} \]
Here, θ is the angle that the magnetic field makes with the horizontal.

4. **Analyzing the Angle at the Equator**:
At the equator, since the magnetic field lines are parallel to the surface, the angle θ approaches 0. Therefore, we can write:
\[ \theta \to 0 \implies \tan(\theta) \to 0 \]

5. **Implications of the Angle Approaching Zero**:
If \(\tan(\theta)\) approaches 0, then:
\[ \frac{BV}{BH} \to 0 \]
This implies that the vertical component (BV) is much smaller than the horizontal component (BH).

6. **Conclusion**:
Since the vertical component of the magnetic field is negligible at the equator, we conclude that:
\[ BH \gg BV \]

### Final Answer:
At a point near the equator, the horizontal component of the magnetic field (BH) is significantly larger than the vertical component (BV).

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