`3 A` of current is flowing in a linear conductor having a length of `40 cm`. The conductor is placed in a magnetic field of strength 500 gauss and makes an angle of `30^(@)` with the direction of the field. It experiences a force of magnitude

Options

A. `3 xx 10^(-4) N`
B. `3 xx 10^(-2) N`
C. `3 xx 10^(2) N`
D. `3 xx 10^(-4) N`

Answer

To solve the problem, we need to calculate the force experienced by a current-carrying conductor in a magnetic field. The formula for the force \( F \) on a current-carrying conductor is given by:

\[ F = I \cdot L \cdot B \cdot \sin(\theta) \]

Where:
- \( F \) is the force in Newtons (N)
- \( I \) is the current in Amperes (A)
- \( L \) is the length of the conductor in meters (m)
- \( B \) is the magnetic field strength in Tesla (T)
- \( \theta \) is the angle between the conductor and the magnetic field in degrees

### Step-by-Step Solution

1. **Identify the given values:**
- Current, \( I = 3 \, \text{A} \)
- Length of the conductor, \( L = 40 \, \text{cm} = 0.4 \, \text{m} \) (conversion from cm to m)
- Magnetic field strength, \( B = 500 \, \text{Gauss} \)
- Angle, \( \theta = 30^\circ \)

2. **Convert the magnetic field from Gauss to Tesla:**
- We know that \( 1 \, \text{Gauss} = 10^{-4} \, \text{Tesla} \).
- Therefore, \( B = 500 \, \text{Gauss} = 500 \times 10^{-4} \, \text{T} = 0.05 \, \text{T} \).

3. **Calculate \( \sin(\theta) \):**
- For \( \theta = 30^\circ \), we have:
\[ \sin(30^\circ) = \frac{1}{2} \]

4. **Substitute the values into the formula:**
\[ F = I \cdot L \cdot B \cdot \sin(\theta) \]
\[ F = 3 \, \text{A} \cdot 0.4 \, \text{m} \cdot 0.05 \, \text{T} \cdot \frac{1}{2} \]

5. **Perform the calculations:**
- First, calculate \( 3 \cdot 0.4 \cdot 0.05 \):
\[ 3 \cdot 0.4 = 1.2 \]
\[ 1.2 \cdot 0.05 = 0.06 \]
- Now multiply by \( \frac{1}{2} \):
\[ 0.06 \cdot \frac{1}{2} = 0.03 \, \text{N} \]

6. **Final Result:**
- The force experienced by the conductor is:
\[ F = 0.03 \, \text{N} \]

### Summary
The magnitude of the force experienced by the conductor is \( 0.03 \, \text{N} \).