At a certain location in Africa, compass point `12^(circ)` west of geographic north. The north tip of magnetic needle of a dip circle placed in the plane of magnetic meridian points `60^(circ)` above the horizontal. The horizontal component of the earth's field is measured to be `0.16 (G)`. The magnitude of the earth's field at the location is

Answer

To find the magnitude of the Earth's magnetic field at the given location, we can use the relationship between the horizontal component of the magnetic field and the angle of dip (or inclination). Here's a step-by-step solution:

### Step 1: Understand the Components of the Magnetic Field
The Earth's magnetic field can be resolved into two components:
- The horizontal component (Bh)
- The vertical component (Bv)

The total magnetic field (B) can be calculated using the Pythagorean theorem:
\[ B = \sqrt{B_h^2 + B_v^2} \]

### Step 2: Identify Given Values
From the problem, we have:
- Horizontal component, \( B_h = 0.16 \, \text{G} \)
- Angle of dip (or inclination), \( \theta = 60^\circ \)

### Step 3: Calculate the Vertical Component
The vertical component can be calculated using the angle of dip:
\[ B_v = B \sin(\theta) \]
And since we know that:
\[ B_h = B \cos(\theta) \]
We can express \( B \) in terms of \( B_h \) and \( \theta \):
\[ B = \frac{B_h}{\cos(\theta)} \]

### Step 4: Substitute the Values
Substituting the known values into the equation:
\[ B = \frac{0.16 \, \text{G}}{\cos(60^\circ)} \]

Since \( \cos(60^\circ) = 0.5 \):
\[ B = \frac{0.16 \, \text{G}}{0.5} \]
\[ B = 0.32 \, \text{G} \]

### Step 5: Conclusion
The magnitude of the Earth's magnetic field at the location is:
\[ B = 0.32 \, \text{G} \]