What should be the value of 0 if charge and velocity are constant and the final output of magnetic force should be one ?

Options

A. Zero
B. 90
C. 180
D. 270

Explanation

To solve the problem, we need to determine the value of the angle \( \theta \) such that the magnetic force \( F_m \) is equal to 1, given that the charge \( q \) and the velocity \( v \) are constant. The magnetic force is given by the equation:

\[ F_m = q v B \sin \theta \]

where:
- \( F_m \) is the magnetic force,
- \( q \) is the charge,
- \( v \) is the velocity,
- \( B \) is the magnetic field strength,
- \( \theta \) is the angle between the velocity vector and the magnetic field vector.

### Step-by-Step Solution:

1. **Set up the equation**: We want the magnetic force \( F_m \) to be equal to 1. Therefore, we can write:
\[ q v B \sin \theta = 1 \]

2. **Assume \( q v B = 1 \)**: For simplicity, let's assume that the product \( q v B = 1 \). This simplifies our equation to:
\[ \sin \theta = 1 \]

3. **Determine the angle \( \theta \)**: The sine function equals 1 at:
\[ \theta = 90^\circ \]

4. **Check other options**:
- If \( \theta = 0^\circ \):
\[ \sin 0^\circ = 0 \implies F_m = 0 \quad (\text{not valid}) \]
- If \( \theta = 180^\circ \):
\[ \sin 180^\circ = 0 \implies F_m = 0 \quad (\text{not valid}) \]
- If \( \theta = 270^\circ \):
\[ \sin 270^\circ = -1 \implies F_m = -q v B \quad (\text{not valid since we want a positive force}) \]

5. **Conclusion**: The only angle that satisfies the condition \( F_m = 1 \) is:
\[ \theta = 90^\circ \]

Thus, the value of \( \theta \) should be \( 90^\circ \).