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 problem, we need to analyze the assertion and reason provided regarding the Lorentz force and the transformation of electric and magnetic fields when switching frames of reference.

### Step-by-Step Solution:

1. **Understanding the Lorentz Force**:
The Lorentz force acting on a charge \( q \) moving with velocity \( \vec{v} \) in an electromagnetic field is given by the equation:
\[ \vec{F} = q(\vec{v} \times \vec{B} + \vec{E}) \]
Here, \( \vec{E} \) is the electric field, and \( \vec{B} \) is the magnetic field.

2. **Switching Frames of Reference**:
When we switch to a different inertial frame moving with an instantaneous velocity \( \vec{v} \), we need to consider how the electric and magnetic fields transform. The transformation of fields is governed by the laws of electromagnetism.

3. **Electric and Magnetic Field Transformation**:
In the new frame, the electric field \( \vec{E}' \) and magnetic field \( \vec{B}' \) can be expressed in terms of the original fields \( \vec{E} \) and \( \vec{B} \) as follows:
\[ \vec{E}' = \vec{E} + \vec{v} \times \vec{B} \]
\[ \vec{B}' = \vec{B} - \frac{1}{c^2} (\vec{v} \times \vec{E}) \]
where \( c \) is the speed of light.

4. **Existence of an Appropriate Electric Field**:
In the new frame, the electric field \( \vec{E}' \) includes a term that depends on the velocity \( \vec{v} \) and the magnetic field \( \vec{B} \). This means that there exists an electric field in the new frame that accounts for the motion of the charge.

5. **Conclusion**:
Since both the assertion and reason are true, and the reason correctly explains the assertion, we conclude that:
- The assertion is true: The expression for the Lorentz force holds when switching to a frame with instantaneous velocity \( \vec{v} \).
- The reason is true: There exists an appropriate electric field in the new frame due to the transformation of fields.

### Final Answer:
Both the assertion and reason are true, and the reason is the correct explanation for the assertion.

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