A square coil of `10^(-2) m^(2)` area is placed perpenducular to a uniform magnetic field of `10^(3) Wb//m^(2)`. What is magnetic flux through the coil?

Options

A. (a)10 weber
B. (b)`10^(-5)` weber
C. (c)Zero
D. (d)100 weber

Answer

To solve the problem of finding the magnetic flux through a square coil placed perpendicular to a uniform magnetic field, we can follow these steps:

### Step 1: Understand the formula for magnetic flux
The magnetic flux (Φ) through a surface is given by the formula:
\[ Φ = B \cdot A \cdot \cos(θ) \]
where:
- \(B\) is the magnetic field strength (in Weber per square meter, Wb/m²),
- \(A\) is the area of the coil (in square meters, m²),
- \(θ\) is the angle between the magnetic field and the normal to the surface.

### Step 2: Identify the given values
From the problem statement, we have:
- Area of the coil, \(A = 10^{-2} \, m^2\)
- Magnetic field strength, \(B = 10^3 \, Wb/m^2\)
- Since the coil is placed perpendicular to the magnetic field, the angle \(θ = 0°\).

### Step 3: Calculate the cosine of the angle
The cosine of \(0°\) is:
\[ \cos(0°) = 1 \]

### Step 4: Substitute the values into the formula
Now, we can substitute the values into the magnetic flux formula:
\[ Φ = B \cdot A \cdot \cos(θ) \]
Substituting the known values:
\[ Φ = (10^3 \, Wb/m^2) \cdot (10^{-2} \, m^2) \cdot \cos(0°) \]
\[ Φ = (10^3) \cdot (10^{-2}) \cdot 1 \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ Φ = 10^{3 - 2} = 10^1 = 10 \, Wb \]

### Conclusion
The magnetic flux through the coil is:
\[ Φ = 10 \, Wb \]