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Step-by-Step Explanation
1. Understanding the Fields
A charged particle, in this case an electron, is placed in a region where both the electric field $\vec{E}$ and the magnetic field $\vec{B}$ are uniform and directed along the same line.
2. Force Due to the Magnetic Field
The magnetic force on a charge $q$ moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$ is given by the Lorentz force law:
$$ \vec{F}_{\text{mag}} = q\, (\vec{v} \times \vec{B}). $$
Since the velocity $\vec{v}$ of the electron is parallel to the magnetic field $\vec{B}$ (both are along the same direction), their cross product is zero:
$$ \vec{v} \times \vec{B} = 0. $$
Thus, the magnetic force on the electron is zero in this scenario.
3. Force Due to the Electric Field
The electric force on the electron is given by:
$$ \vec{F}_{\text{elec}} = q \, \vec{E}. $$
Here, $q$ is the charge of the electron, which is negative ($-e$). Even though $\vec{E}$ and $\vec{v}$ point in the same direction, the electron experiences a force in the direction opposite to $\vec{E}$ because its charge is negative. As a result, this force acts opposite to its velocity.
4. Effect on the Electron's Velocity
Because the net force on the electron is opposite to its direction of motion (and there is no magnetic contribution), the electron will slow down. Therefore, its velocity decreases over time due to the influence of the electric field alone.
5. Conclusion
With no magnetic force to balance or alter its path, and an electric force acting against its motion, the electron’s velocity must decrease. Hence, the correct answer is that the electron’s velocity will decrease.
