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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 and Reason are true and the Reason is correct explanation of the Assertion.

B

If both assertion and reason are true but Reason is not the correct explanation of the Assertion.

C

If Assertion is true, but the Reason is false.

D

If both assertion and reason are false

Text Solution

AI Generated Solution

The correct Answer is:
To solve the given question, we need to analyze the assertion and reason provided regarding the behavior of a proton and an electron in a uniform electric field. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that a proton and an electron placed in the same uniform electric field experience different accelerations. - This is based on the fact that both particles have different masses and will respond differently to the same electric force. 2. **Electric Force Calculation**: - The electric force \( F \) acting on a charge \( q \) in an electric field \( E \) is given by the formula: \[ F = qE \] - For the proton (charge \( +e \)): \[ F_{proton} = eE \] - For the electron (charge \( -e \)): \[ F_{electron} = -eE \] - Both particles experience forces of equal magnitude but in opposite directions. 3. **Acceleration Calculation**: - According to Newton's second law, the acceleration \( a \) of an object is given by: \[ a = \frac{F}{m} \] - For the proton: \[ a_{proton} = \frac{F_{proton}}{m_{proton}} = \frac{eE}{m_{proton}} \] - For the electron: \[ a_{electron} = \frac{F_{electron}}{m_{electron}} = \frac{-eE}{m_{electron}} \] - Since the mass of the proton \( m_{proton} \) is much larger than the mass of the electron \( m_{electron} \), the accelerations will differ significantly. 4. **Conclusion on the Assertion**: - Since \( m_{proton} \) is much greater than \( m_{electron} \), it follows that: \[ a_{proton} < a_{electron} \] - Thus, the assertion that they experience different accelerations is **true**. 5. **Understanding the Reason**: - The reason states that the electric force on a test charge is independent of its mass. - This is true because the force depends only on the charge and the electric field, not on the mass of the charge. 6. **Linking Assertion and Reason**: - While both the assertion and reason are true, the reason does not explain why the proton and electron experience different accelerations. The difference in acceleration arises due to their different masses, not because the force is independent of mass. ### Final Conclusion: - The assertion is true, and the reason is true, but the reason is **not the correct explanation** for the assertion.

To solve the given question, we need to analyze the assertion and reason provided regarding the behavior of a proton and an electron in a uniform electric field. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that a proton and an electron placed in the same uniform electric field experience different accelerations. - This is based on the fact that both particles have different masses and will respond differently to the same electric force. ...
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