A charge is moving through a magnetic field. The force acting on the charge is maximum when the angle between the velocity of charge and the magnetic field is _______

Answer

To find the angle between the velocity of a charge and the magnetic field at which the force acting on the charge is maximum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Situation**:
A charged particle is moving through a magnetic field. The force acting on the charged particle due to the magnetic field is given by the Lorentz force formula.

2. **Lorentz Force Formula**:
The magnetic force \( F \) acting on a charge \( q \) moving with a velocity \( v \) in a magnetic field \( B \) is given by:
\[ F = q(v \times B) = qvB \sin \theta \]
where \( \theta \) is the angle between the velocity vector \( v \) and the magnetic field vector \( B \).

3. **Maximizing the Force**:
To find when the force is maximum, we need to maximize the term \( \sin \theta \). The sine function reaches its maximum value of 1 when \( \theta = 90^\circ \) (or \( \frac{\pi}{2} \) radians).

4. **Conclusion**:
Therefore, the magnetic force acting on the charge is maximum when the angle \( \theta \) between the velocity of the charge and the magnetic field is:
\[ \theta = 90^\circ \text{ or } \frac{\pi}{2} \]

### Final Answer:
The angle between the velocity of charge and the magnetic field is \( 90^\circ \) or \( \frac{\pi}{2} \).

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