A pair of horizontal plates are situated in a vacuum and separated by a distance of 1.8cm. What potential energy would need to be connected across the plates in order to hold a single electron suspended at rest between them?

Ans:
I used the formula
(qv)/d = mg ; where q=is the charge on the electron, d is the distance in metres; m is the mass and g is the gravitational constant on earth.

i get 1.00540...*10^-12

is this the correct answer??

Your equation is correct.

You do not provide any dimensions to go with your number. I would mark it incorrect for that reason alone.

Also, I assume that they are asking for a potential difference (energy per charge in Volts or J/C, not a potential energy. They are not the same thing.

V = m g D/e = 9.8*10^-31 kg*9.8m/s^2*0.018 m/1.6*10^-19 C
= 1.1*10^-12 Volts

You were on the right track; we nearly agree on the number. I did not keep many significant figures.

No, your approach and formula are not correct for this scenario.

To find the potential energy needed to hold a single electron suspended between two plates, you need to consider the electric potential energy equation.

The electric potential energy (PE) between two plates separated by a distance (d) is given by:

PE = qV

Where q is the charge of the electron (-1.6 x 10^-19 coulombs) and V is the potential difference (in volts) between the plates.

In this case, you are given the distance between the plates (d = 1.8 cm = 0.018 m). However, you are not given the potential difference.

To find the potential difference, you need to consider the electric field and voltage between the plates. In a uniform electric field, the potential difference between two points is given by:

V = Ed

Where E is the electric field strength.

To hold the electron suspended at rest, the electrostatic force (Fe) acting on it must be equal and opposite to the gravitational force (Fg) acting on the electron.

Fe = Fg

The electrostatic force can be calculated using the formula:

Fe = qE

Where E is the electric field strength. The electric field strength (E) can be calculated using the formula:

E = V/d

Substituting the values, Fe = q(V/d).

Setting Fe equal to Fg gives:

q(V/d) = mg

Substituting the values for the charge of the electron (q) and the mass of the electron (m), and solving for V, we can then use the value of V to calculate the potential energy (PE).

The correct calculation should give a different result than what you obtained.

To find the potential energy required to hold a single electron suspended at rest between the plates, we need to consider the electric potential energy rather than gravitational potential energy since we are dealing with charges.

The formula you used, (qv)/d = mg, is actually the equation that relates electric force (qv)/d to the weight (mg) of an object. However, in this case, we need to calculate the electric potential energy.

The electric potential energy of a point charge q in an electric field created by two parallel plates is given by the equation:

PE = qV

where PE is the electric potential energy, q is the charge of the electron, and V is the potential difference (voltage) applied across the plates.

To find the potential energy needed to hold a single electron suspended at rest between the plates, we first need to convert the distance between the plates from centimeters to meters. Since 1 centimeter is equal to 0.01 meters, the distance becomes:

d = 1.8 cm = 0.018 m

The charge of an electron q is approximately -1.6 x 10^-19 C.

Now, we need to find the potential difference (V) required. We can use the formula:

V = Ed

where E is the electric field strength between the plates.

The electric field strength (E) between the plates is given by:

E = V/d

Since the plates are in a vacuum, the electric field strength is equal to the potential difference. Hence, we have:

E = V

Substituting the values:

V = Ed = 0.018 m x E

Now, we can equate the electric force and gravitational force on the electron:

(qV)/d = mg

Solving for V gives us:

V = (mgd)/q

Substituting the values:

V = ((9.8 m/s^2) x (0.018 m))/(-1.6 x 10^-19 C)

Calculating this expression will give you the potential difference (V) required.

Once you have the value of V, you can then calculate the potential energy PE using the equation:

PE = qV

where q is the charge of the electron and V is the potential difference.

After performing the calculations, you should obtain the correct value for the potential energy required to hold a single electron suspended at rest between the plates.