In this example we will calculate the work done on an electron moving in a unifo

Question

In this example we will calculate the work done on an electron moving in a uniform electric field. Two large conducting plates separated by 6.36 mm carry charges of equal magnitude and opposite sign, creating a constant electric field with magnitude 2.80×103N/C between the plates. An electron moves from the negatively charged plate to the positively charged plate. How much work does the electric field do on the electron?

In the same problem, how much work does the electric field do on the electron if the magnitude of the field is increased to 5.30×103N/C, and the separation between the plates is reduced to 3.53 mm ?

Explanation / Answer

Here distance between the plates, d = 6.36 mm and the electric field = 2800 N/C
So the potential difference = E*d = 2800*6.36*10^-3 = 17.8 V.
a)
So the work done by electric field,
W = q*deltaV = -1.6*10^-19*17.8 = -17.8 eV = -2.848*10^-18 J.
b)
The potential difference in this case, delta V = E*d = 5300 * 3.53*10^-3 = 18.7 V.
hence work done will be,
W = -18.7 eV = -2.993*10^-18 J.

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