Final answer:
The speed of the electron as it emerges from the field is 3.00 × 10^6 m/s.
Step-by-step explanation:
The question mentions an electron passing between two charged metal plates that create a vertical electric field. The initial speed of the electron is given as 3.00 × 10^6 m/s, and the horizontal distance it travels in the uniform field is 4.00 cm. The question asks for the speed of the electron as it emerges from the field, if it just misses the upper plate.
To find the speed of the electron, we need to consider the effect of the electric field on its motion. The electric field will cause the electron to experience a vertical deflection. We can use the equations for constant acceleration to solve this problem.
First, we need to find the vertical deflection of the electron. Since the initial velocity of the electron is only horizontal, the vertical deflection will be zero. Therefore, the electron just misses the upper plate.
Since the vertical deflection is zero, the vertical component of the final velocity is also zero. Therefore, the speed of the electron as it emerges from the field is the same as its initial speed, which is 3.00 × 10^6 m/s.