Question

A proton and an electron are placed in an uniform electric field

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

Answer 1

The correct option is B

The magnitudes of the electric forces acting on them will be equal

The explanation for the correct answer

1. Let us write the force on a charged body when placed in an external electric field.
   The force $\overrightarrow{F}$ experienced by a particle having a charge $q$ when placed in an external electric field $\overrightarrow{E}$ is given by
   $\overrightarrow{F}=q\overrightarrow{E}-\left(1\right)$
2. Formula used:
   $\overrightarrow{F}=q\overrightarrow{E}$
3. Now, let us analyze the question.
   Let the forces on the proton and electron when placed in the external electric field $\overrightarrow{E}$ be $\overrightarrow{F_p}$ and $\overrightarrow{F_e}$ respectively.
   The charge on the proton is $+e=+1.602\times {10}^{-19}C$while the charge on the electron is $-e=-1.602\times {10}^{-19}C$.
   Therefore, using (1), we get
   $\overrightarrow{F_p}=+e\overrightarrow{E}$
   $\overrightarrow{F_e}=-e\overrightarrow{E}$
4. Comparing $\overrightarrow{F_P}$ and $\overrightarrow{F_e}$, we can see that
   $\overrightarrow{F_p}=-\overrightarrow{F_e}$
   Hence, the forces on the proton and the electron are not equal.
   However, if we consider the magnitudes, we get
   $\left|\overrightarrow{F_p}\right|=\left|-\overrightarrow{F_e}\right|$
   Therefore, the magnitudes of the forces on the proton and the electron are equal.

The explanation for the incorrect option:

Option A: the electric forces acting on them will be equal

1. Now, let us analyze the question.
   Let the forces on the proton and electron when placed in the external electric field $\overrightarrow{E}$ be $\overrightarrow{F_p}$ and $\overrightarrow{F_e}$ respectively.
   The charge on the proton is $+e=+1.602\times {10}^{-19}C$while the charge on the electron is $-e=-1.602\times {10}^{-19}C$.
   Therefore, using (1), we get
   $\overrightarrow{F_p}=+e\overrightarrow{E}$
   $\overrightarrow{F_e}=-e\overrightarrow{E}$
2. Comparing $\overrightarrow{F_P}$ and $\overrightarrow{F_e}$, we can see that
   $\overrightarrow{F_p}=-\overrightarrow{F_e}$
   Hence, the forces on the proton and the electron are not equal.

Option C: Their accelerations will be equal

1. The acceleration will be in the direction of the force and since the forces on the electron and the proton will be in the opposite directions, their accelerations will also be in opposite directions and hence will not be equal.

Option D: The magnitudes of their accelerations will be equal

1. The acceleration will be in the direction of the force and since the forces on the electron and the proton will be in the opposite directions, their accelerations will also be in opposite directions and hence will not be equal.
2. Also, the magnitudes will also not be equal even though the magnitudes of the forces are equal.
3. This is because the magnitude of the acceleration will be the ratio of the magnitude of the force to the mass.
4. Since the masses of the electron and proton are different, so even though the magnitudes of the forces on them are equal, the magnitudes of their accelerations will not be equal.

The correct option is B) The magnitude of the electric forces will be equal.