A proton and an electron are placed in a uniform electric field. Which of the following is correct?

Options

A. The electric force acting on them will be equal
B. The magnitudes of the forces will be equal
C. Their acceleration will be equal
D. The magnitudes of their accelerations will be equal

Explanation

To solve the problem of determining the correct statement regarding a proton and an electron placed in a uniform electric field, we will analyze the forces acting on both particles and their resulting accelerations.

### Step-by-Step Solution:

1. **Understanding Electric Charge**:
- A proton has a positive charge of \( +1.6 \times 10^{-19} \) coulombs.
- An electron has a negative charge of \( -1.6 \times 10^{-19} \) coulombs.

2. **Electric Force Calculation**:
- The electric force (\( F \)) acting on a charged particle in an electric field (\( E \)) is given by the formula:
\[ F = qE \]
- For the electron:
\[ F_e = -qE = -(-1.6 \times 10^{-19})E = 1.6 \times 10^{-19}E \quad \text{(in the direction opposite to the electric field)} \]
- For the proton:
\[ F_p = qE = (1.6 \times 10^{-19})E \quad \text{(in the direction of the electric field)} \]

3. **Comparing Forces**:
- The magnitudes of the forces acting on both particles are equal:
\[ |F_e| = |F_p| = 1.6 \times 10^{-19}E \]
- However, the directions of the forces are opposite. Therefore, the statement that the forces are equal in magnitude is correct, but they act in opposite directions.

4. **Acceleration Calculation**:
- The acceleration (\( a \)) of a particle is given by Newton's second law:
\[ a = \frac{F}{m} \]
- The mass of the electron (\( m_e \)) is approximately \( 9.11 \times 10^{-31} \) kg, and the mass of the proton (\( m_p \)) is approximately \( 1.67 \times 10^{-27} \) kg.
- For the electron:
\[ a_e = \frac{F_e}{m_e} = \frac{1.6 \times 10^{-19}E}{9.11 \times 10^{-31}} \quad \text{(in the direction opposite to the electric field)} \]
- For the proton:
\[ a_p = \frac{F_p}{m_p} = \frac{1.6 \times 10^{-19}E}{1.67 \times 10^{-27}} \quad \text{(in the direction of the electric field)} \]

5. **Comparing Accelerations**:
- Since the masses of the proton and electron are different, their accelerations will also be different. Therefore, the magnitudes of their accelerations are not equal.

### Conclusion:
- The correct statement is that the magnitudes of the forces acting on the proton and electron are equal, but their directions are opposite. The accelerations of the proton and electron are not equal due to their different masses.