A doubly charged ion is accelerated to an energy of 34.0 keV by the electric field between two parallel conducting plates separated by 2.00 cm. What is the electric field strength between the plates?
To find the electric field strength (E) between two parallel conducting plates, we can use the formula:
E = V / d
where:
E is the electric field strength,
V is the potential difference between the plates,
and d is the separation distance between the plates.
In this case, we are given the potential difference V as 34.0 keV (kiloelectron volts) and the separation distance d as 2.00 cm.
First, we need to convert the potential difference from keV to volts by multiplying it by the conversion factor 1 keV = 1.6 x 10^-19 J:
V = 34.0 keV * (1.6 x 10^-19 J/1 keV)
V = 5.44 x 10^-18 J
Next, we need to convert the separation distance from centimeters to meters by dividing it by 100:
d = 2.00 cm / 100
d = 0.0200 m
Now, we can substitute the values into the formula to find the electric field strength:
E = V / d
E = (5.44 x 10^-18 J) / (0.0200 m)
E ≈ 2.72 x 10^-16 N/C
Therefore, the electric field strength between the plates is approximately 2.72 x 10^-16 N/C.