Question

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

• A. Electrical forces acting on them will be equal
• B. Magnitude of the electrical forces will be equal
• C. Their acceleration will be equal
• D. Magnitude of their acceleration will be equal.

Answer 1

The correct option is B Magnitude of the electrical forces will be equal

Suppose the electric field intensity is $E$, then the force at any charge is given by,

$\overrightarrow{F}=q\overrightarrow{E}$

For proton:

Force, $\overrightarrow{F_p}=e\overrightarrow{E}......\left(1\right)$

$\Rightarrow |\overrightarrow{F_p}|=|e\overrightarrow{E}|........\left(2\right)$

Acceleration of proton,

$\overrightarrow{a_p}=\frac{e\overrightarrow{E}}{m_P}...........\left(3\right)$

For electron:

Force, $\overrightarrow{F_e}=-e\overrightarrow{E}.......\left(4\right)$

$\Rightarrow |\overrightarrow{F_e}|=|-e\overrightarrow{E}|=|e\overrightarrow{E}|.......\left(5\right)$

Now,acceleration of electron,

$\overrightarrow{a_e}=\frac{-e\overrightarrow{E}}{m_e}........\left(6\right)$

From eqs.(1) and (4),
Elecrtric forces are directed in opposite directions.

But from eqs. (2) and (3),
they have equal magnitudes.

From eqs. (3) and (6),
Accelerations are directed in opposite directions and also magnitudes are not equal as mass of proton $\left(m_P\right)$ is not equal to mass of electron $m_e)$.

Hence, option $\left(b\right)$ is correct.