When an electron is projected into a region where both a uniform electric field and a uniform magnetic field are present, and both fields are aligned in the same direction as the electron's velocity, we need to analyze the forces acting on the electron to determine its motion. The key here is to understand how electric and magnetic fields influence charged particles like electrons.
Understanding the Forces at Play
First, let's break down the forces acting on the electron:
- Electric Force: The electric field exerts a force on the electron given by the equation Fe = qE, where q is the charge of the electron (which is negative) and E is the strength of the electric field. Since the electric field is directed in the same direction as the electron's velocity, the electric force will act in the same direction as the velocity, causing the electron to accelerate.
- Magnetic Force: The magnetic field exerts a force on the electron according to the equation Fm = q(v × B), where v is the velocity of the electron and B is the magnetic field. The direction of the magnetic force is determined by the right-hand rule. Since the electron has a negative charge, the magnetic force will act in the opposite direction to what the right-hand rule would suggest.
Analyzing the Direction of Forces
Given that both fields are aligned in the same direction as the velocity of the electron:
- The electric force will increase the velocity of the electron because it acts in the same direction.
- The magnetic force, however, will act perpendicular to both the velocity and the magnetic field. This means it will not contribute to the increase or decrease of the speed of the electron but will instead cause the electron to change direction.
Resulting Motion of the Electron
Since the electric force accelerates the electron in the direction of the fields, while the magnetic force causes a change in direction, the overall effect is that:
- The electron's speed will increase due to the electric force.
- The magnetic force will cause the electron to move in a circular path or spiral, depending on the relative strengths of the electric and magnetic fields.
Final Conclusion
Based on this analysis, the correct answer to your question is:
- c) The electron's velocity will increase in magnitude.
In summary, while the magnetic field affects the direction of the electron's path, the electric field contributes to an increase in the electron's speed. This interplay of forces is fundamental in understanding the behavior of charged particles in electromagnetic fields.
