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 The magnetic flux linked with the disc is

Options

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

Explanation

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

### Step 1: Understand the formula for magnetic flux
Magnetic flux (Φ) is given by the formula:
\[ \Phi = \mathbf{B} \cdot \mathbf{A} = B \cdot A \cdot \cos(\theta) \]
where:
- \( \Phi \) is the magnetic flux,
- \( B \) is the magnetic field induction (in Wb/m²),
- \( A \) is the area of the surface (in m²),
- \( \theta \) is the angle between the magnetic field and the normal (perpendicular) to the surface.

### Step 2: Calculate the area of the circular 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 \( r = 0.2 \, m \):
\[ A = \pi (0.2)^2 = \pi (0.04) = 0.04\pi \, m^2 \]

### Step 3: Identify the magnetic field induction and angle
The magnetic field induction \( B \) is given as:
\[ B = \frac{1}{\pi} \, \text{Wb/m}^2 \]
The angle \( \theta \) between the magnetic field and the normal to the disc is given as \( 60^\circ \).

### Step 4: Calculate the magnetic flux
Now, substituting the values into the magnetic flux formula:
\[ \Phi = B \cdot A \cdot \cos(60^\circ) \]
We know that \( \cos(60^\circ) = \frac{1}{2} \):
\[ \Phi = \left(\frac{1}{\pi}\right) \cdot (0.04\pi) \cdot \frac{1}{2} \]

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

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

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