An electron moving in an electric potential field $V_{1}$ enters a higher electric potential field $V_{2}$, then the change in kinetic energy of the electron is proportional to

Question

Accepted Answer

When an electron moves from one electric potential field to another, its kinetic energy changes due to the work done by the electric field. The change in kinetic energy of the electron is directly related to the difference in electric potential between the two fields.

1. **Explanation for Option 2: $(V_{2}-V_{1})$**

The change in kinetic energy of an electron moving between two electric potentials is given by the equation:
   $$
   \Delta KE = -e(V_{2} - V_{1})
   $$
   where $ e $ is the charge of the electron. This equation shows that the change in kinetic energy is directly proportional to the difference in electric potential, $ (V_{2} - V_{1}) $. Therefore, Option 2 is correct because it accurately represents the linear relationship between the change in kinetic energy and the potential difference.

2. **Explanation for why other options are incorrect:**

- **Option 1: $\sqrt{(V_{2}-V_{1})}$**

This option suggests that the change in kinetic energy is proportional to the square root of the potential difference. However, the relationship between kinetic energy change and potential difference is linear, not a square root function. Therefore, this option is incorrect.

- **Option 3: $(V_{2}-V_{1})^{2}$**

This option implies that the change in kinetic energy is proportional to the square of the potential difference. The equation for kinetic energy change does not involve squaring the potential difference; it is a linear relationship. Thus, this option is incorrect.

- **Option 4: $\frac{1}{\sqrt{(V_{2}-V_{1})}}$**

This option suggests an inverse square root relationship between the change in kinetic energy and the potential difference. There is no physical basis for such a relationship in the context of electric potential and kinetic energy change. Therefore, this option is incorrect.

In conclusion, Option 2 is the correct answer because it accurately reflects the direct proportionality between the change in kinetic energy of an electron and the difference in electric potential, as described by the fundamental principles of electromagnetism.