The vertical deflecting plates of a typical classroom oscilloscope are a pair of parallel square metal plates carrying equal but opposite charges. The potential difference between the plates is 25.0 V. Typical dimensions are about 3.3 cm on a side, with a separation of about 5.0 mm. The plates are close enough that we can ignore fringing at the ends. Part A: Under these conditions, how much charge is on each plate?(Express your answer in coulombs.) Part B: How strong is the electric field between the plates?(Express your answer in volts per meter.) Part C:If an electron is ejected at rest from the negative plates, how fast is it moving when it reaches the positive plate?(Express your answer in meters per second.)
The vertical deflecting plates of a typical classroom oscilloscope are a pair of parallel square metal plates carrying equal but opposite charges. The potential difference between the plates is 25.0 V. Typical dimensions are about 3.3 cm on a side, with a separation of about 5.0 mm. The plates are close enough that we can ignore fringing at the ends.
Part A: Under these conditions, how much charge is on each plate?(Express your answer in coulombs.)
Part B: How strong is the electric field between the plates?(Express your answer in volts per meter.)
Part C:If an electron is ejected at rest from the negative plates, how fast is it moving when it reaches the positive plate?(Express your answer in meters per second.)
To find the charge on each plate, we can use the formula for the capacitance (C) of a parallel-plate capacitor:
C = (ε₀ × A) / d
Where:
- C is the capacitance,
- ε₀ (epsilon naught) is the vacuum permittivity constant ( 8.85×10⁻¹² F/m),
- A is the area of one plate, (0.033)2 m²
- d is the separation between the plates=5.0 mm = 0.005 m
Now, calculate the capacitance (C):
C = (8.85×10-12 × 0.0332 )/ 0.005
C= 1.93×10-12 F
The charge (Q) on each plate of the capacitor is related to the capacitance and potential difference by the formula:
Q = C×V
Potential difference (V) = 25.0 V
Q=1.93×10-12×25.0
Q=48.19×10-12 C
So, the charge on each plate is approximately 48.19×10-12 Coulombs.
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