A current of `10` ampere is flowing in a wire of length `1.5m`. A force of `15 N` acts on it when it is placed in a uniform magnetic field of `2` tesla. The angle between the magnetic field and the direction of the current is

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

To find the angle between the magnetic field and the direction of the current in a wire, we can use the formula for the force acting on a current-carrying wire in a magnetic field:

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

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

### Step 1: Identify the given values
From the problem, we have:
- \( F = 15 \, \text{N} \)
- \( I = 10 \, \text{A} \)
- \( L = 1.5 \, \text{m} \)
- \( B = 2 \, \text{T} \)

### Step 2: Rearrange the formula to solve for \( \sin(\theta) \)
We can rearrange the formula to isolate \( \sin(\theta) \):

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

### Step 3: Substitute the known values into the equation
Now, substitute the known values into the equation:

\[ \sin(\theta) = \frac{15}{10 \cdot 1.5 \cdot 2} \]

### Step 4: Calculate the denominator
Calculate \( I \cdot L \cdot B \):

\[ I \cdot L \cdot B = 10 \cdot 1.5 \cdot 2 = 30 \]

### Step 5: Calculate \( \sin(\theta) \)
Now substitute this back into the equation for \( \sin(\theta) \):

\[ \sin(\theta) = \frac{15}{30} = \frac{1}{2} \]

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

\[ \theta = \sin^{-1}\left(\frac{1}{2}\right) \]

From trigonometric values, we know:

\[ \theta = 30^\circ \]

### Conclusion
Thus, the angle between the magnetic field and the direction of the current is \( 30^\circ \).