Two capacitor plates are equally and oppositely charged. They are separated by 1.30 cm.

An electron is released from rest at the surface of the negative plate and, at the same time, a proton is released from rest at the surface of the positive plate.

Where do the electron and proton pass each other? Give your answer as a distance from the positive plate.

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To determine where the electron and proton pass each other, we need to analyze the motion of the particles in the electric field between the capacitor plates.

To do this, we'll need to calculate the electric field created by the charged capacitor plates. The electric field between two parallel plates of a capacitor can be approximated as a uniform field. The equation for the electric field between the plates is given by:

E = V / d

where E is the electric field, V is the potential difference between the plates, and d is the distance between the plates.

Given that the plates are separated by 1.30 cm, we need to calculate the electric field.

Now, to determine the potential difference between the plates, we need to use the formula:

V = Ed

where V is the potential difference, E is the electric field, and d is the distance between the plates.

Once we have the potential difference, we can use it to calculate the final velocity of the particles using the equation:

v = sqrt((2*q*V) / m)

where v is the final velocity of the particles, q is the charge of the particles (in this case, the charge of an electron and a proton), V is the potential difference, and m is the mass of the particles (in this case, the mass of an electron and a proton).

Now that we have the final velocity, we can calculate the distance at which the electron and proton pass each other. Since they are released from rest at the surfaces of the respective plates, we can assume the initial velocity of the particles is zero. Using the equation of motion:

d = (v^2) / (2 * a)

where d is the distance, v is the final velocity of the particles, and a is the acceleration of the particles.

The acceleration of the particles can be calculated using the equation:

a = q * E / m

where a is the acceleration, q is the charge of the particles, E is the electric field, and m is the mass of the particles.

With all these calculations, we can find the distance at which the electron and proton pass each other, starting from the positive plate.