A proton beam is fired from west to east and an electron beam is fired parallel to it in the same direction. Force on the electron beam will be

Options

A. upwards
B. downwards
C. towards the proton beam
D. away from the proton beam

Explanation

To solve the problem of determining the force on the electron beam fired parallel to a proton beam, we can follow these steps:

### Step 1: Understand the scenario
We have two beams: a proton beam moving from west to east and an electron beam moving in the same direction (east). The proton beam generates a magnetic field due to its motion.

### Step 2: Determine the magnetic field produced by the proton beam
The magnetic field \( \mathbf{B} \) produced by a moving charge (the protons in this case) can be calculated using the Biot-Savart law. The direction of the magnetic field produced by a moving positive charge is given by the right-hand rule.

- For a proton moving from west to east, the magnetic field will be directed in a circular manner around the path of the proton. Above the proton beam (where the electron beam is located), the magnetic field will point downward.

### Step 3: Analyze the force on the electron beam
The force \( \mathbf{F} \) on a charged particle moving in a magnetic field is given by the Lorentz force law:
\[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \]
where \( q \) is the charge of the particle, \( \mathbf{v} \) is its velocity, and \( \mathbf{B} \) is the magnetic field.

- The electron has a negative charge \( (-e) \) and is moving in the same direction as the protons (eastward).

### Step 4: Apply the right-hand rule to find the direction of the force
1. **Velocity of the electron**: Point your fingers in the direction of the electron's velocity (east).
2. **Magnetic field direction**: Curl your fingers downward (the direction of the magnetic field above the proton beam).
3. **Force direction**: Your thumb will point in the direction of the force acting on a positive charge. Since the electron has a negative charge, the force will be in the opposite direction.

### Step 5: Conclude the direction of the force on the electron beam
Since the thumb points upward for a positive charge, the force on the negatively charged electron will be directed downward. However, because of the negative charge, the actual force on the electron will be directed **upward**, away from the proton beam.

### Final Answer
The force on the electron beam will be directed **upward** and **away from the proton beam**.

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