A vertical wire carries a current in upward direction. An electron beam sent horizontally towards the wire will be deflected

Options

A. towards right
B. towards left
C. upwards
D. downwards

Answer

To solve the problem of how an electron beam is deflected when sent horizontally towards a vertical wire carrying an upward current, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Direction of Current**:
The wire carries a current in the upward direction.

**Hint**: Remember that the direction of current is defined as the direction in which positive charges would move.

2. **Determine the Direction of the Magnetic Field**:
According to the right-hand rule, if you point your thumb in the direction of the current (upward), your fingers will curl around the wire in the direction of the magnetic field. For a vertical wire with upward current, the magnetic field will circulate around the wire. Below the wire, the magnetic field direction will be towards you (out of the plane of the paper).

**Hint**: Use the right-hand rule to visualize the magnetic field direction around the wire.

3. **Identify the Direction of Electron Beam**:
The electron beam is sent horizontally towards the wire. Since electrons are negatively charged, their velocity vector will be in the opposite direction to that of a positive charge.

**Hint**: Remember that the velocity of the electron beam is horizontal and directed towards the wire.

4. **Apply the Lorentz Force Law**:
The force on a charged particle moving in a magnetic field is given by the equation:
\[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \]
where \( q \) is the charge of the particle, \( \mathbf{v} \) is the velocity vector, and \( \mathbf{B} \) is the magnetic field vector.

5. **Determine the Cross Product**:
Since the electron has a negative charge, we need to consider the direction of the force. The velocity vector \( \mathbf{v} \) is towards the wire (let's assume to the right), and the magnetic field \( \mathbf{B} \) is out of the plane of the paper (towards you).

Using the right-hand rule for the cross product \( \mathbf{v} \times \mathbf{B} \):
- Point your fingers in the direction of \( \mathbf{v} \) (to the right).
- Curl your fingers in the direction of \( \mathbf{B} \) (out of the plane).
- Your thumb will point downwards, indicating the direction of the force for a positive charge.

Since the electron is negatively charged, the force will be in the opposite direction, which is upwards.

**Hint**: Remember to reverse the direction of the force when dealing with negative charges.

6. **Conclusion**:
The electron beam will be deflected upwards as it approaches the wire due to the magnetic force acting on it.

**Final Answer**: The electron beam will be deflected upwards.