The force acting on a charge 'q' moving with a velocity V in a magnetic field of induction B is given by

Options

A. `(q)/(vecV xx vecB)`
B. `vecV xx vec B)/(q)`
C. `q(vecV xx vecB)`
D. `(vecV. vecB) q`

Answer

To solve the question regarding the force acting on a charge 'q' moving with a velocity 'V' in a magnetic field of induction 'B', we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept**: The force acting on a charged particle moving in a magnetic field is described by the Lorentz force law. The force \( \mathbf{F} \) on a charge \( q \) moving with a velocity \( \mathbf{V} \) in a magnetic field \( \mathbf{B} \) is given by the equation:
\[ \mathbf{F} = q (\mathbf{V} \times \mathbf{B}) \]
where \( \times \) denotes the cross product.

2. **Identify the Parameters**:
- \( q \) is the charge of the particle.
- \( \mathbf{V} \) is the velocity vector of the charge.
- \( \mathbf{B} \) is the magnetic field vector.

3. **Direction of the Force**: The direction of the force can be determined using the right-hand rule. If you point your fingers in the direction of \( \mathbf{V} \) and curl them towards \( \mathbf{B} \), your thumb will point in the direction of the force \( \mathbf{F} \).

4. **Magnitude of the Force**: The magnitude of the force can be calculated as:
\[ F = qV B \sin \theta \]
where \( \theta \) is the angle between the velocity vector \( \mathbf{V} \) and the magnetic field vector \( \mathbf{B} \).

5. **Final Expression**: Therefore, the force acting on the charge can be expressed as:
\[ \mathbf{F} = q (\mathbf{V} \times \mathbf{B}) = qV B \sin \theta \]

### Conclusion:
The force acting on a charge \( q \) moving with a velocity \( V \) in a magnetic field \( B \) is given by:
\[ \mathbf{F} = q (\mathbf{V} \times \mathbf{B}) \]
or in terms of magnitude:
\[ F = qV B \sin \theta \]