Question

An electron is fired at a speed V₀ = 5.6 x 10⁶ m/s and at an angle θ₀ = -45 degree between two parallel conducting plates that are d= 2.0 mm apart. If the voltage difference between the plates is △V = 100 V

Determine (a) how close, d, the electron will get to the bottom plate and (b) where the electron will strike the top plate.

Answer 1

To determine how close the electron will be to the bottom plate, we can use the equations of motion and electric field.

The electric field between the plates can be found using the equation E = ΔV/d, where ΔV is the voltage difference and d is the distance between the plates. To find where the electron will strike the top plate, we can use the equations of motion and electric field again.

Step-by-step explanation:

To determine how close the electron will be to the bottom plate, we can use the equations of motion and electric field. The electric field between the plates can be found using the equation E = ΔV/d, where ΔV is the voltage difference and d is the distance between the plates.

In this case, E = (100 V)/(0.002 m) = 50000 V/m. Next, we can find the vertical acceleration of the electron using the equation F = qE, where F is the force, q is the charge of the electron, and E is the electric field. Since the force is equal to the weight of the electron (mg), we have mg = qE, where m is the mass of the electron and g is the acceleration due to gravity.

The distance the electron will fall can be found using the equation s = 0.5at^2, where s is the vertical distance, a is the acceleration, and t is the time. Since the initial vertical velocity of the electron is 0, the time it takes to fall can be found using the equation t = sqrt(2s/a).

To find where the electron will strike the top plate, we can use the equations of motion and electric field again. The horizontal distance the electron travels can be found using the equation s = ut + 0.5at^2, where s is the horizontal distance, u is the initial horizontal velocity, a is the horizontal acceleration (which is 0 in this case), and t is the time.

The time it takes for the electron to travel the horizontal distance can be found using the equation t = d/u, where d is the distance between the plates and u is the initial horizontal velocity. Finally, the vertical distance the electron will be deflected can be found using the equation s = 0.5at^2, where s is the vertical distance, a is the vertical acceleration, and t is the time.