A thin bar magnet of length 2L is bent at the mid point, so that the angle between them is `60^(@)`.Find the new length of the magnet.

Options

A. `sqrt(2)L`
B. `sqrt(3)L`
C. 2L
D. L

Answer

To find the new length of a thin bar magnet that has been bent at its midpoint to form an angle of 60 degrees, we can follow these steps:

### Step 1: Understand the Initial Configuration
The initial length of the bar magnet is given as \( 2L \). When it is bent at the midpoint, each half of the magnet will have a length of \( L \).

### Step 2: Visualize the Bending
When the magnet is bent at the midpoint to form an angle of 60 degrees, we can visualize the two halves of the magnet forming a "V" shape. Each half makes an angle of 30 degrees with the vertical line drawn from the midpoint.

### Step 3: Calculate the New Length
To find the new effective length of the magnet, we can use the cosine of the angle formed by each half of the magnet with respect to the vertical.

The new length \( L' \) can be calculated using the formula:
\[ L' = L \cos(30^\circ) + L \cos(30^\circ) \]
Since there are two halves, we multiply the length of one half by 2.

### Step 4: Substitute the Cosine Value
We know that:
\[ \cos(30^\circ) = \frac{\sqrt{3}}{2} \]
Thus, substituting this value into our equation:
\[ L' = 2L \cos(30^\circ) = 2L \left(\frac{\sqrt{3}}{2}\right) \]
This simplifies to:
\[ L' = L \sqrt{3} \]

### Step 5: Conclusion
The new length of the magnet after bending is:
\[ L' = L \sqrt{3} \]