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A uniform electric field and a uniform m...

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity then

A

speed will decrease

B

speed will increase

C

will run towards left of direction of motion

D

will turn towards right of direction of motion

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the forces acting on the electron when it is projected in the presence of both electric and magnetic fields that are aligned in the same direction. ### Step-by-Step Solution: 1. **Identify the Forces Acting on the Electron**: - The electron has a negative charge, denoted as \( q = -e \). - The electric field \( E \) exerts an electric force \( F_e \) on the electron given by the equation: \[ F_e = qE = -eE \] - The magnetic force \( F_m \) on a charged particle moving in a magnetic field is given by: \[ F_m = q(\mathbf{v} \times \mathbf{B}) \] - Here, \( \mathbf{v} \) is the velocity of the electron and \( \mathbf{B} \) is the magnetic field. Since both the velocity and the magnetic field are in the same direction, the angle \( \theta \) between them is \( 0^\circ \). 2. **Calculate the Magnetic Force**: - The magnetic force can be expressed as: \[ F_m = -e(\mathbf{v} \times \mathbf{B}) \] - Since \( \mathbf{v} \) and \( \mathbf{B} \) are parallel, the cross product \( \mathbf{v} \times \mathbf{B} = 0 \). Therefore, the magnetic force \( F_m \) is: \[ F_m = 0 \] 3. **Determine the Net Force on the Electron**: - The only force acting on the electron is the electric force \( F_e \): \[ F_{net} = F_e + F_m = -eE + 0 = -eE \] - This indicates that the net force is directed opposite to the direction of the electric field. 4. **Effect on the Electron's Velocity**: - The negative electric force acting on the electron will cause it to decelerate. Since the force is in the opposite direction to the velocity, the speed of the electron will decrease over time. 5. **Conclusion**: - Therefore, the correct answer is that the speed of the electron will decrease. ### Final Answer: The speed of the electron will decrease.
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