A particle of charge q and mass `m` is moving along the x-axis with a velocity `v` and enters a region of electric field `E` and magnetic field `B` as shown in figures below. For which figure the net force on the charge may be zero?

Options

A.
B.
C.
D.

Explanation

To determine for which figure the net force on the charged particle may be zero, we need to analyze the forces acting on the particle due to the electric field \(E\) and the magnetic field \(B\).

### Step-by-Step Solution:

1. **Identify the Forces**:
- The force due to the electric field \(E\) on a charge \(q\) is given by:
\[ F_E = qE \]
- The force due to the magnetic field \(B\) when the particle is moving with velocity \(v\) is given by:
\[ F_B = q(v \times B) \]
- The net force \(F_{net}\) on the charge is the vector sum of these two forces:
\[ F_{net} = F_E + F_B \]

2. **Condition for Zero Net Force**:
- For the net force to be zero, the forces must be equal in magnitude and opposite in direction:
\[ F_E + F_B = 0 \quad \Rightarrow \quad F_E = -F_B \]

3. **Analyze Each Figure**:
- In each figure, we need to check the orientation of the electric field \(E\) and the magnetic field \(B\) relative to the velocity \(v\) of the particle.
- The electric field \(E\) will exert a force in the direction of the field, while the magnetic field \(B\) will exert a force that is perpendicular to both the velocity \(v\) and the magnetic field \(B\) (as determined by the right-hand rule).

4. **Determine the Correct Configuration**:
- If \(E\) is directed along the positive y-axis and \(B\) is directed into the page (negative z-axis), then using the right-hand rule, the magnetic force \(F_B\) will act in the negative y-direction.
- In this case, the forces can balance each other out if their magnitudes are equal, leading to a net force of zero.

5. **Conclusion**:
- The figure where the electric field \(E\) and magnetic field \(B\) are oriented such that \(F_E\) and \(F_B\) are equal in magnitude and opposite in direction will result in a net force of zero on the charged particle.