A conductor of length 20 cm carries a current of 1A is kept at an angle with the magnetic field of 4T. Find the angle between the conductor and the magnetic field if it experiences a force of 0.4 N.

Options

A. `0^@`
B. `30^@`
C. `60^@`
D. `90^@`

Answer

To solve the problem, we need to use the formula for the force experienced by a current-carrying conductor in a magnetic field. The formula is given by:

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

Where:
- \( F \) is the force on the conductor (in Newtons),
- \( I \) is the current through the conductor (in Amperes),
- \( L \) is the length of the conductor (in meters),
- \( B \) is the magnetic field strength (in Teslas),
- \( \theta \) is the angle between the conductor and the magnetic field.

### Step 1: Convert the length of the conductor to meters
The length of the conductor is given as 20 cm. We need to convert this to meters:

\[ L = 20 \, \text{cm} = 20 \times 10^{-2} \, \text{m} = 0.2 \, \text{m} \]

**Hint:** Remember that 1 cm = 0.01 m, so to convert cm to m, multiply by \( 10^{-2} \).

### Step 2: Identify the known values
From the problem, we have:
- Current, \( I = 1 \, \text{A} \)
- Length, \( L = 0.2 \, \text{m} \)
- Magnetic field, \( B = 4 \, \text{T} \)
- Force, \( F = 0.4 \, \text{N} \)

### Step 3: Substitute the known values into the formula
Now we can substitute the known values into the formula:

\[ 0.4 = 1 \cdot 0.2 \cdot 4 \cdot \sin(\theta) \]

### Step 4: Simplify the equation
Calculating the right-hand side:

\[ 0.4 = 0.8 \cdot \sin(\theta) \]

### Step 5: Solve for \( \sin(\theta) \)
Now, we can isolate \( \sin(\theta) \):

\[ \sin(\theta) = \frac{0.4}{0.8} = 0.5 \]

### Step 6: Find the angle \( \theta \)
To find \( \theta \), we take the inverse sine:

\[ \theta = \sin^{-1}(0.5) \]

The angle whose sine is 0.5 is:

\[ \theta = 30^\circ \]

### Final Answer
The angle between the conductor and the magnetic field is \( 30^\circ \).

---