Oscilloscopes have parallel metal plates inside them to deflect the electron beam. These plates are called the deflecting plates. Typically, they are squares 3.0 cm on a side and separated by 5.0 mm, with very thin air in between. What is the capacitance of these deflecting plates and hence of the oscilloscope?

Question

Oscilloscopes have parallel metal plates inside them to deflect the electron beam. These plates are called the deflecting plates. Typically, they are squares 3.0 cm on a side and separated by 5.0 mm, with very thin air in between. What is the capacitance of these deflecting plates and hence of the oscilloscope?

Express your answer using two significant figures.
-------------------
Using C = epsilon*area / distance:
C = (8.854e-12)(3e-2)^2 / (5e-3)
C = 1.59372e-12 or 1.6e-12
but this isn't correct.
Am I missing something? This is the only capacitance equation that uses area and distance.

Answer 1

the deflection is vertical AND horizontal

... two sets of plates

the "thin air" in the question is basically vacuum ... check your epsilon value

Answer 2

It seems like you're on the right track by using the formula C = ε * A / d to calculate the capacitance of the deflecting plates. However, it looks like there was a small calculation mistake in your calculations.

Let's go through the calculations again step by step:

Given:
ε (epsilon) = 8.854e-12 F/m (permittivity of free space)
A (area) = (3.0 cm)^2 = 9.0e-4 m^2 (Remember to convert cm to meters)
d (distance) = 5.0 mm = 5.0e-3 m

Now plug in these values into the formula:

C = ε * A / d
C = (8.854e-12 F/m) * (9.0e-4 m^2) / (5.0e-3 m)

Now let's calculate this expression:

C = 1.59712e-14 F or approximately 1.6e-14 F (using two significant figures)

So the capacitance of the deflecting plates would be approximately 1.6e-14 F, not 1.6e-12 F as you have calculated before.

Please double-check your calculations and make sure you have used the correct values for the area and distance.