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Uniform electric and magnetic fields are...

Uniform electric and magnetic fields are produced in the same direction. An electron moves in such a way that its velocity remains in the direction of electric field. The electron will-

A

turn towards left

B

turn towards right

C

get decelerated

D

get accelerated

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AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the motion of an electron in the presence of uniform electric and magnetic fields that are aligned in the same direction. Here’s a step-by-step solution: ### Step 1: Understand the Forces Acting on the Electron In this scenario, two forces are acting on the electron: 1. **Electric Force (Fe)**: This force is given by the equation: \[ F_e = qE \] where \( q \) is the charge of the electron (which is negative) and \( E \) is the electric field strength. 2. **Magnetic Force (Fm)**: This force is given by the equation: \[ F_m = q(\mathbf{v} \times \mathbf{B}) \] where \( \mathbf{v} \) is the velocity of the electron and \( \mathbf{B} \) is the magnetic field strength. ### Step 2: Determine the Direction of the Forces - Since the electric field and the magnetic field are in the same direction, we can denote them as \( \mathbf{E} \) and \( \mathbf{B} \). - The electron, being negatively charged, will experience a force due to the electric field in the opposite direction of the field. Thus, the electric force \( \mathbf{F_e} \) will act opposite to the direction of \( \mathbf{E} \). ### Step 3: Analyze the Magnetic Force - The magnetic force depends on the cross product of the velocity \( \mathbf{v} \) and the magnetic field \( \mathbf{B} \). Since the velocity of the electron is in the same direction as the electric field (and hence the magnetic field), the angle \( \theta \) between \( \mathbf{v} \) and \( \mathbf{B} \) is 0 degrees. - The sine of 0 degrees is 0, which means: \[ F_m = qvB \sin(0) = 0 \] - Therefore, the magnetic force acting on the electron is zero. ### Step 4: Conclusion on the Electron's Motion - Since the only force acting on the electron is the electric force \( \mathbf{F_e} \), and this force is directed opposite to the motion of the electron, the electron will experience a deceleration. - As a result, the electron will slow down as it moves in the direction of the electric field. ### Final Answer The correct conclusion is that the electron will get decelerated.

To solve the problem, we need to analyze the motion of an electron in the presence of uniform electric and magnetic fields that are aligned in the same direction. Here’s a step-by-step solution: ### Step 1: Understand the Forces Acting on the Electron In this scenario, two forces are acting on the electron: 1. **Electric Force (Fe)**: This force is given by the equation: \[ F_e = qE \] ...
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