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Assetrion: If a proton and electron are ...

Assetrion: If a proton and electron are placed in the same uniform electric field. They experience different acceleration
Reason: Electric force on a test charge is independent of its mass

A

If both Assertion `&` Reason are True `&` the Reason is a correct explanation of the Assertion.

B

If both Assertion `&` Reason are True but Reason is not a correct explanation of the Assertion.

C

If Assertion is True but the Reason is False.

D

If both Assertion `&` Reason are False.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion and the reason provided: **Assertion:** If a proton and electron are placed in the same uniform electric field, they experience different acceleration. **Reason:** Electric force on a test charge is independent of its mass. ### Step-by-Step Solution: 1. **Understanding Electric Force:** The electric force \( F \) experienced by a charge \( q \) in an electric field \( E \) is given by the equation: \[ F = qE \] Here, both the proton and electron have the same magnitude of charge, which is approximately \( 1.6 \times 10^{-19} \) coulombs. 2. **Calculating Forces on Proton and Electron:** Since both the proton and electron have the same charge magnitude: \[ F_{\text{proton}} = eE \quad \text{and} \quad F_{\text{electron}} = eE \] Thus, the magnitudes of the forces acting on both particles are equal. 3. **Using Newton's Second Law:** According to Newton's second law, the acceleration \( a \) of an object is given by: \[ a = \frac{F}{m} \] where \( F \) is the force acting on the object and \( m \) is its mass. 4. **Calculating Acceleration:** - For the electron: \[ a_{\text{electron}} = \frac{F_{\text{electron}}}{m_{\text{electron}}} = \frac{eE}{m_{\text{electron}}} \] - For the proton: \[ a_{\text{proton}} = \frac{F_{\text{proton}}}{m_{\text{proton}}} = \frac{eE}{m_{\text{proton}}} \] 5. **Comparing Accelerations:** Since the mass of the electron is significantly less than that of the proton (\( m_{\text{electron}} < m_{\text{proton}} \)), it follows that: \[ a_{\text{electron}} > a_{\text{proton}} \] Therefore, the proton and electron experience different accelerations when placed in the same uniform electric field. 6. **Evaluating the Assertion and Reason:** - The assertion is **true** because the proton and electron do indeed experience different accelerations. - The reason is **not a correct explanation** for the assertion. While the electric force is indeed independent of mass, the acceleration depends on the mass of the charge. Thus, the reason does not adequately explain why the assertion is true. ### Conclusion: The assertion is true, but the reason is not a correct explanation for the assertion.

To solve the question, we need to analyze the assertion and the reason provided: **Assertion:** If a proton and electron are placed in the same uniform electric field, they experience different acceleration. **Reason:** Electric force on a test charge is independent of its mass. ### Step-by-Step Solution: ...
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