(A) : Free electrons always keep on moving in a conductor even then no magnetic force act on them in magnetic field unless a current is passed through it.
(R) : The average velocity of free electron in a conductor is zero in the absence of the electric field in it.

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. 'A' is true and 'R' is false
D. 'A' is false and 'R' is false

Answer

To solve the given question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states: "Free electrons always keep on moving in a conductor even then no magnetic force acts on them in a magnetic field unless a current is passed through it."

- Free electrons in a conductor are indeed in constant motion due to thermal energy. However, this motion is random, and there is no net movement in any specific direction unless an external electric field is applied, which causes a drift velocity.

### Step 2: Analyze the Reason
The reason states: "The average velocity of free electron in a conductor is zero in the absence of the electric field in it."

- In the absence of an electric field, the free electrons move randomly in all directions. As a result, their average velocity sums to zero. This means that while individual electrons are moving, there is no net flow of charge, which is what constitutes an electric current.

### Step 3: Connect the Assertion and Reason
- The assertion claims that no magnetic force acts on the free electrons unless there is a current. The reason explains that the average velocity of these electrons is zero without an electric field, which means there is no current.

- Since the assertion is true (no current means no magnetic force) and the reason is also true (average velocity is zero without an electric field), and the reason correctly explains the assertion, we conclude that both statements are true and the reason is the correct explanation for the assertion.

### Conclusion
Both the assertion and the reason are true, and the reason is the correct explanation for the assertion.

### Final Answer
- Assertion (A) is true.
- Reason (R) is true.
- R is the correct explanation of A.

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