The figure shows an electron entering a parallel-plate capacitor with a speed of 5.65×106 . The electric field of the capacitor has deflected the electron downward by a distance of 0.618 at the point where the electron exits the capacitor.

An electron is launched at a 45∘ angle and a speed of 5.0×106m/s from the positive plate of the parallel-plate capacitor shown in the figure (Figure 1) . The electron lands 4.0 cm away.

Part A
What is the electric field strength inside the capacitor?

The first thing you should learn about physics is that you have to provide the dimensions along with the numbers when computing physical quantities. Physics is not just arithmetic.

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To find the electric field strength of the parallel-plate capacitor, we can use the given information about the electron's motion and the distance it is deflected.

1. Start by identifying the known values:
- Initial speed of the electron, vi = 5.65×10^6 m/s
- Distance deflected, d = 0.618 m

2. The force experienced by an electron in an electric field is given by the equation:
F = qE
where F is the force, q is the charge of the electron, and E is the electric field strength.

3. The force acting on the electron is due to the deflection caused by the electric field. The force is given by Newton's second law of motion:
F = m * a
where m is the mass of the electron and a is the acceleration.

4. Since the electron is moving horizontally, the net force acting on it is in the vertical direction. Therefore, we can assume that the force due to the electric field provides the necessary vertical acceleration. Using the equation of motion:
d = (1/2) * a * t^2 (since the initial velocity of the electron is zero in the vertical direction)
where d is the distance deflected, a is the acceleration, and t is the time taken for the deflection.

5. Rearrange the equation to solve for the time, t:
t = sqrt(2d / a)

6. Now, we need to find the acceleration, a. We can calculate it using Newton's second law of motion:
F = m * a
qE = m * a
a = (qE) / m

7. Substitute the expression for acceleration into the time equation:
t = sqrt(2d / ((qE) / m))

8. Finally, we can solve for the electric field strength, E:
E = (q*t) / d

Using the given values for the electron's speed and distance deflected, and the known charge and mass of an electron, you can substitute these values into the equation to calculate the electric field strength of the parallel-plate capacitor.

3550 N/C