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

Options

A. the elective forces acting on them will be equal
B. their acceleration will be equal
C. the magnitude of the forces will be equal
D. the magnitude of their acceleration will be equal

Answer

To solve the problem of comparing the forces and accelerations of a proton and an electron placed in a uniform electric field, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Electric Field and Forces**:
- In a uniform electric field, the electric field lines originate from positive charges and terminate on negative charges.
- The force experienced by a charged particle in an electric field is given by the formula:
\[ F = Q \cdot E \]
where \( F \) is the force, \( Q \) is the charge of the particle, and \( E \) is the electric field strength.

2. **Identifying Charges**:
- The charge of a proton is \( +q = +1.602 \times 10^{-19} \) coulombs.
- The charge of an electron is \( -q = -1.602 \times 10^{-19} \) coulombs.

3. **Calculating Forces**:
- For the proton:
\[ F_p = Q_p \cdot E = (+q) \cdot E = +1.602 \times 10^{-19} \cdot E \]
- For the electron:
\[ F_e = Q_e \cdot E = (-q) \cdot E = -1.602 \times 10^{-19} \cdot E \]

4. **Direction of Forces**:
- The force on the proton is directed towards the negative side (opposite to the direction of the electric field).
- The force on the electron is directed towards the positive side (in the direction of the electric field).

5. **Comparing Magnitudes**:
- The magnitudes of the forces are:
\[ |F_p| = |F_e| = 1.602 \times 10^{-19} \cdot E \]
- Therefore, the magnitudes of the forces acting on the proton and electron are equal.

6. **Calculating Acceleration**:
- The acceleration \( a \) of an object is given by Newton's second law:
\[ a = \frac{F}{m} \]
- The mass of the proton \( m_p \) is approximately \( 1.67 \times 10^{-27} \) kg, and the mass of the electron \( m_e \) is approximately \( 9.11 \times 10^{-31} \) kg.
- The accelerations are:
\[ a_p = \frac{F_p}{m_p} = \frac{1.602 \times 10^{-19} \cdot E}{1.67 \times 10^{-27}} \]
\[ a_e = \frac{F_e}{m_e} = \frac{1.602 \times 10^{-19} \cdot E}{9.11 \times 10^{-31}} \]
- Since the masses are different, the accelerations will not be equal.

7. **Final Conclusion**:
- The forces on the proton and electron are equal in magnitude but opposite in direction.
- Their accelerations are not equal due to the difference in their masses.

### Summary of Correct Options:
- The magnitude of the forces on the proton and electron are equal.
- The forces are not equal in direction, and hence their accelerations are also not equal.