Question

A proton and an electron are released from rest in the center of a capacitor.

A) Is the force ratio Fp/Fe greater than 1, less than 1, or equal to 1?

B) Is the acceleration ratio ap/ae greater than 1, less than 1, or equal to 1?

Answer 1

The force ratio Fp/Fe when a proton and an electron are released in a capacitor is equal to 1, as they experience the same magnitude of force. The acceleration ratio ap/ae is less than 1 because the proton is more massive and thus accelerates less under the same force.

Step-by-step explanation:

When a proton and an electron are released from rest in the center of a capacitor, the force ratio Fp/Fe (force on proton to force on electron) is equal to 1. This is because the magnitude of the charge on a proton and an electron is the same (just opposite in sign), and the force experienced by a charge in an electric field is given by F = qE, where q is the charge and E is the electric field strength. Hence the electric forces on both the proton and the electron are equal in magnitude but opposite in direction.

As for the acceleration ratio ap/ae (acceleration of proton to acceleration of electron), it is less than 1. This occurs because acceleration is defined by a = F/m, where F is the force and m is the mass of the particle. Since the proton has a much greater mass than the electron, for the same magnitude of force, the acceleration of the proton will be much smaller than that of the electron.

Answer 2

a) equal 1, b) less than 1

Step-by-step explanation:

a) the electric force is given by

Fe = q E

The charge of the electron and proton has the same value, that of the proton is positive and that of the electron is negative

Proton

Fp = qE

Electron

Fe = - q E

Fp / Fe = -1

If we do not take into account the sign the relationship is equal to one (1)

b) to calculate the force we use Newton's second law

F = ma

qE = m a

a = q E / m

The mass of the proton much greater than the mass of the electron

ap = q E /
`m_(p)`

ae = - q E /
`m_(e)`

ap / ae =
`m_(e)` /
`m_(p)` =
`m_(e)`/1600
`m_(e)` =1/1600

It is much smaller than 1