A circular disc of radius `0.2 m` is placed in a uniform magnetic fied of induction `(1)/(pi) ((Wb)/(m^(2)))`
in such a way that its axis makes an angle of `60^(@)` with `B`. The magnetic flux linked with the disc is

Options

A. 0.02Wb
B. 0.06Wb
C. 0.08Wb
D. 0.01Wb

Explanation

To find the magnetic flux linked with a circular disc placed in a magnetic field, we can follow these steps:

### Step 1: Calculate the Area of the Disc
The area \( A \) of a circular disc is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the disc.

Given:
- Radius \( r = 0.2 \, m \)

Substituting the value of \( r \):
\[ A = \pi (0.2)^2 = \pi (0.04) = 0.04\pi \, m^2 \]

### Step 2: Use the Magnetic Flux Formula
The magnetic flux \( \Phi \) linked with the disc is given by the formula:
\[ \Phi = B A \cos \theta \]
where:
- \( B \) is the magnetic field induction,
- \( A \) is the area of the disc,
- \( \theta \) is the angle between the magnetic field and the normal to the surface of the disc.

Given:
- \( B = \frac{1}{\pi} \, \text{Wb/m}^2 \)
- \( \theta = 60^\circ \)

### Step 3: Calculate \( \cos \theta \)
We need to find \( \cos 60^\circ \):
\[ \cos 60^\circ = \frac{1}{2} \]

### Step 4: Substitute Values into the Flux Formula
Now, substituting the values into the flux formula:
\[ \Phi = \left(\frac{1}{\pi}\right) \left(0.04\pi\right) \left(\frac{1}{2}\right) \]

### Step 5: Simplify the Expression
Now, simplify the expression:
\[ \Phi = \frac{1}{\pi} \cdot 0.04\pi \cdot \frac{1}{2} = 0.04 \cdot \frac{1}{2} = 0.02 \, \text{Wb} \]

### Conclusion
Thus, the magnetic flux linked with the disc is:
\[ \Phi = 0.02 \, \text{Wb} \]

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