Easy problem from Electrostatics

A charge of 20 μ \mu C produces an electric field. Two points are 10cm and 5cm from this charge. Find the amount of work done to take an electron from one point to the other. ——————————————————————————————
Please answer in SI units

1.44e-13 2.88e-13 2.88e-14 1.44e-14

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1 solution

Miss Physicist
Mar 5, 2019

Let A and B be two points at distance 10cm and 5cm from the charge.
V A a n d V B V_{A} and V_{B} are values of potential at these points.
Now, V A V_{A} = 1 4 π ϵ q r 1 = 9 1 0 9 20 1 0 6 0.1 = 1.8 1 0 6 V \frac{1}{4\pi\epsilon}*\frac{q}{r_{1}}=9*10^{9}*\frac{20*10^{-6}}{0.1}=1.8*10^{6}V
Similarly if we calculate V B V_{B} it comes out to be 3.6 1 0 6 V 3.6*10^{6}V
Difference between V A a n d V B V_{A} and V_{B} is 1.8 1 0 6 1.8*10^6 V.
Work done to take the electron from A to B is 1.8 1 0 6 1.6 1 0 19 = 2.88 1 0 13 J 1.8*10^{6}*1.6*10^{-19}=\boxed{2.88*10^{-13}J}

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