In: Physics

# How much does the electric potential energy change as the electron moves from i to f?

n electron (q=-e) completes half of a circular orbit of radius r around a nucleus with Q=+3e.

a. How much work is done on the electron as it moves from i to f? Give either a numerical value if you knew the radius. Justify your answer.

b. By how much does the electric potential energy change as the electron moves from i to f?

c. Is the electron's speed at f greater than, less than, or equal to its speed at i?

## Solutions

##### Expert Solution

(a) The distance of the electron from the charge $$Q$$ is same at all points of its motion. That is from $$i$$ to $$f$$. So the potential is the same. The work done is, $$W=q \Delta V$$

$$\begin{array}{l} =q(0) \\ =0 \end{array}$$

(b) The distance of the electron from the charge $$Q$$ is the same at all points of its motion. That is from $$i$$ to $$f$$. So the potential is the same. Hence the electric potential energy is, $$\Delta U=W$$

$$=0$$

(c) Apply law of conservation of energy. The change in potential energy is zero. Hence,

\begin{aligned} K_{f} &=K_{i} \\ \frac{1}{2} m v_{f}^{2} &=\frac{1}{2} m v_{i}^{2} \\ v_{f} &=v_{i} \end{aligned}

Thus, the final speed is equal to the initial speed.