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 solve the question, we need to determine the angle at which the magnetic force acting on a moving charge is maximized. Let's break this down step by step.

### Step 1: Understand the Magnetic Force Formula
The magnetic force \( F_m \) acting on a charge \( Q \) moving with velocity \( V \) in a magnetic field \( B \) is given by the formula:
\[ F_m = Q (V \times B) \]
This can also be expressed in terms of the angle \( \theta \) between the velocity vector \( V \) and the magnetic field vector \( B \):
\[ F_m = Q V B \sin \theta \]

### Step 2: Identify the Components of the Formula
In the formula \( F_m = Q V B \sin \theta \):
- \( Q \) is the charge (constant for a given particle),
- \( V \) is the speed of the charge (constant),
- \( B \) is the magnetic field strength (constant),
- \( \theta \) is the angle between the velocity vector and the magnetic field vector.

### Step 3: Determine When the Force is Maximum
The force \( F_m \) depends on \( \sin \theta \). The sine function reaches its maximum value of 1 when:
\[ \sin \theta = 1 \]
This occurs when:
\[ \theta = 90^\circ \]

### Step 4: Conclusion
Thus, the magnetic force acting on the charge is maximum when the angle between the velocity of the charge and the magnetic field is:
\[ \theta = 90^\circ \]

### Final Answer
The angle between the velocity of charge and the magnetic field is **90 degrees**.

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