MHT CET · Physics · Electrostatics
An electron of mass ' \(m_e\) ' and a proton of mass ' \(m_p\) ' are kept in a uniform electric field. The ratio of the acceleration of electron \(\left(a_e\right)\) to the acceleration of proton \(\left(a_p\right)\) is
- A \(\frac{\mathrm{m}_{\mathrm{e}}}{\mathrm{m}_{\mathrm{p}}}\)
- B \(\frac{\mathrm{m}_{\mathrm{p}}}{\mathrm{m}_{\mathrm{e}}}\)
- C one
- D infinity
Answer & Solution
Correct Answer
(B) \(\frac{\mathrm{m}_{\mathrm{p}}}{\mathrm{m}_{\mathrm{e}}}\)
Step-by-step Solution
Detailed explanation
Electrostatic force, \(\mathrm{F}_{\mathrm{E}}=\mathrm{eE}\) (for both the particles)
The acceleration of electron, \(a_e=\frac{F_E}{M_e}\) and
Acceleration of proton \(a_p=\frac{F_E}{M_e}\)
\(\therefore \frac{\mathrm{a}_{\mathrm{e}}}{\mathrm{a}_{\mathrm{p}}}=\frac{\mathrm{M}_{\mathrm{p}}}{\mathrm{M}_{\mathrm{e}}}\)
The acceleration of electron, \(a_e=\frac{F_E}{M_e}\) and
Acceleration of proton \(a_p=\frac{F_E}{M_e}\)
\(\therefore \frac{\mathrm{a}_{\mathrm{e}}}{\mathrm{a}_{\mathrm{p}}}=\frac{\mathrm{M}_{\mathrm{p}}}{\mathrm{M}_{\mathrm{e}}}\)
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