Assertion: When radius of circular loop carrying current is doubled, its magnetic moment becomes four times.
Rrason: Magnetic moment depends on area of the loop.

Options

A. If both Assertain and Reason are true and Reason is the correct explanation of Assertain
B. If both Assertain and Reason are true but Reason is not correct explantion of Assertain
C. If Assertion is true but Reason is false
D. If Assertion is false but Reason in true.

Explanation

To solve the problem, we need to analyze the assertion and reason provided in the question step by step.

### Step 1: Understanding the Assertion
The assertion states that when the radius of a circular loop carrying current is doubled, the magnetic moment becomes four times.

**Magnetic Moment Formula**:
The magnetic moment (M) for a circular loop is given by the formula:
\[ M = I \times A \]
where \( I \) is the current and \( A \) is the area of the loop.

### Step 2: Area of the Circular Loop
The area \( A \) of a circular loop is calculated using the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the loop.

### Step 3: Initial Magnetic Moment Calculation
For the initial radius \( r \):
\[ M = I \times A = I \times \pi r^2 \]

### Step 4: New Radius Calculation
When the radius is doubled, the new radius becomes \( 2r \). We can now calculate the new area \( A' \):
\[ A' = \pi (2r)^2 = \pi \times 4r^2 = 4\pi r^2 \]

### Step 5: New Magnetic Moment Calculation
Now, substituting the new area into the magnetic moment formula:
\[ M' = I \times A' = I \times 4\pi r^2 = 4 \times (I \times \pi r^2) = 4M \]

### Step 6: Conclusion on the Assertion
From the calculations, we see that when the radius is doubled, the magnetic moment indeed becomes four times the original magnetic moment. Therefore, the assertion is **true**.

### Step 7: Understanding the Reason
The reason states that the magnetic moment depends on the area of the loop.

### Step 8: Analyzing the Reason
As we derived earlier, the magnetic moment is directly proportional to the area of the loop:
\[ M \propto A \]
Thus, the reason is also **true**.

### Step 9: Relationship Between Assertion and Reason
While both the assertion and reason are true, the reason does not provide the correct explanation for the assertion. The assertion specifically states that the magnetic moment becomes four times when the radius is doubled, while the reason only states that magnetic moment depends on the area.

### Final Conclusion
The correct answer is that both the assertion and reason are true, but the reason is not the correct explanation for the assertion.