The magnetic needle of a tangent galvanometer is deflected at an angle `30^(@)` due to a magnet. The hoeizontal component of earth's magnetic field `0.34xx10^(-4)T` is along the plane of the coil. The magnetic intensity is

Options

A. `1.96X10^(-4)T`
B. `5.9X10^(-4)T`
C. `5.9X10^(-5)T`
D. `5.9X10^(5)T`

Answer

To solve the problem, we need to find the magnetic intensity (B) using the information provided about the tangent galvanometer. Here’s the step-by-step solution:

### Step 1: Understand the given values
We are given:
- The deflection angle (θ) = 30 degrees
- The horizontal component of Earth's magnetic field (BH) = 0.34 × 10^(-4) T

### Step 2: Use the formula for magnetic intensity
The magnetic intensity (B) in the horizontal plane can be calculated using the formula:
\[ B = B_H \cdot \tan(\theta) \]

### Step 3: Calculate the tangent of the angle
We need to find the tangent of the angle θ:
\[ \tan(30^\circ) = \frac{1}{\sqrt{3}} \approx 0.577 \]

### Step 4: Substitute the values into the formula
Now, we can substitute the values into the formula:
\[ B = 0.34 \times 10^{-4} \, T \cdot \tan(30^\circ) \]
\[ B = 0.34 \times 10^{-4} \, T \cdot 0.577 \]

### Step 5: Perform the multiplication
Calculating this gives:
\[ B = 0.34 \times 0.577 \times 10^{-4} \]
\[ B \approx 0.196 \times 10^{-4} \, T \]

### Step 6: Convert to scientific notation
To express this in scientific notation:
\[ B \approx 1.96 \times 10^{-5} \, T \]

### Step 7: Conclusion
Thus, the magnetic intensity is:
\[ B \approx 1.96 \times 10^{-5} \, T \]

### Final Answer
The magnetic intensity is \( 1.96 \times 10^{-5} \, T \).

---