a proton placed in an electric field would experience an electrical force equal to its weight. the magnitude of electric field intensity E would be

Options

A. `m^2g/e`
B. `e^2m^2/g`
C. mg/e
D. e/mg

Answer

To solve the problem, we need to find the magnitude of the electric field intensity \( E \) such that the electric force experienced by a proton is equal to its weight.

### Step-by-Step Solution:

1. **Understand the Forces Involved**:
- The weight of the proton can be expressed as:
\[ W = m \cdot g \]
where \( m \) is the mass of the proton and \( g \) is the acceleration due to gravity.

2. **Electric Force on the Proton**:
- The electric force \( F_e \) experienced by a proton in an electric field \( E \) is given by:
\[ F_e = q \cdot E \]
where \( q \) is the charge of the proton. The charge of a proton is equal to the elementary charge \( e \).

3. **Equating the Forces**:
- According to the problem, the electric force is equal to the weight of the proton:
\[ F_e = W \]
Therefore, we can write:
\[ q \cdot E = m \cdot g \]

4. **Substituting the Charge of the Proton**:
- Substitute \( q \) with \( e \) (the charge of the proton):
\[ e \cdot E = m \cdot g \]

5. **Solving for Electric Field Intensity \( E \)**:
- Rearranging the equation to find \( E \):
\[ E = \frac{m \cdot g}{e} \]

6. **Final Expression**:
- The magnitude of the electric field intensity \( E \) that would cause the proton to experience an electric force equal to its weight is:
\[ E = \frac{m \cdot g}{e} \]