A: In the expression for Lorentza force, `vecF=q(vecvxxvecB+vecE)`. If one switches to a frame with instantaneous velcoity `vecv`
R: There exists an appropriate electric field in the new frame.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark 2.
C. If assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the question regarding the Lorentz force and the transformation to a frame with instantaneous velocity, we can break it down into several steps:

### Step-by-Step Solution:

1. **Understanding the Lorentz Force**:
The Lorentz force is given by the equation:
\[ \vec{F} = q(\vec{v} \times \vec{B} + \vec{E}) \]
where:
- \( \vec{F} \) is the total force acting on the charge,
- \( q \) is the charge,
- \( \vec{v} \) is the velocity of the charge,
- \( \vec{B} \) is the magnetic field,
- \( \vec{E} \) is the electric field.

2. **Switching Frames**:
When we switch to a frame moving with an instantaneous velocity \( \vec{v} \), we need to consider how the electric and magnetic fields transform. In this new frame, the magnetic field \( \vec{B} \) may change, and an electric field \( \vec{E}' \) can be introduced.

3. **Electric Field in the New Frame**:
According to the principles of electromagnetism, if we are in a frame moving with velocity \( \vec{v} \), there can be an induced electric field \( \vec{E}' \) that arises due to the motion through the magnetic field. The relationship can be expressed as:
\[ \vec{E}' = -\vec{v} \times \vec{B} \]
This means that in the new frame, the electric field is related to the velocity and the magnetic field.

4. **Resulting Lorentz Force in the New Frame**:
In the new frame, the Lorentz force can still be expressed as:
\[ \vec{F}' = q(\vec{v} \times \vec{B} + \vec{E}') \]
Substituting for \( \vec{E}' \):
\[ \vec{F}' = q(\vec{v} \times \vec{B} - \vec{v} \times \vec{B}) = 0 \]
This shows that the force acting on the charge can be zero if the electric field is appropriately defined.

5. **Conclusion**:
The assertion states that if one switches to a frame with instantaneous velocity \( \vec{v} \), there exists an appropriate electric field in the new frame. This is indeed true, as the transformation of fields ensures that the Lorentz force can still be applied correctly in the new frame.

### Final Answer:
Both the assertion and reason are true, and the reason correctly explains the assertion. Therefore, the correct answer is option A.

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