To find the magnetic flux through the coil, we can follow these steps:
### Step 1: Convert the area from cm² to m²
The area of the coil is given as \(5 \, \text{cm}^2\). To convert this to square meters, we use the conversion factor \(1 \, \text{cm}^2 = 10^{-4} \, \text{m}^2\).
\[
\text{Area} = 5 \, \text{cm}^2 \times 10^{-4} \, \text{m}^2/\text{cm}^2 = 5 \times 10^{-4} \, \text{m}^2
\]
### Step 2: Convert the magnetic field from Gauss to Tesla
The magnetic field is given as \(10^3 \, \text{Gauss}\). To convert this to Tesla, we use the conversion factor \(1 \, \text{Gauss} = 10^{-4} \, \text{Tesla}\).
\[
B = 10^3 \, \text{Gauss} \times 10^{-4} \, \text{Tesla/Gauss} = 0.1 \, \text{Tesla}
\]
### Step 3: Use the formula for magnetic flux
The formula for magnetic flux (\(\Phi\)) through a coil is given by:
\[
\Phi = N \cdot B \cdot A \cdot \cos(\theta)
\]
Where:
- \(N\) = number of turns (20 turns)
- \(B\) = magnetic field (0.1 Tesla)
- \(A\) = area of the coil (\(5 \times 10^{-4} \, \text{m}^2\))
- \(\theta\) = angle between the normal to the coil and the magnetic field (60°)
### Step 4: Calculate \(\cos(60^\circ)\)
The cosine of \(60^\circ\) is:
\[
\cos(60^\circ) = \frac{1}{2}
\]
### Step 5: Substitute the values into the flux formula
Now substituting the values into the formula:
\[
\Phi = 20 \cdot 0.1 \cdot (5 \times 10^{-4}) \cdot \frac{1}{2}
\]
### Step 6: Calculate the flux
Calculating the above expression step by step:
\[
\Phi = 20 \cdot 0.1 = 2
\]
\[
\Phi = 2 \cdot (5 \times 10^{-4}) = 10 \times 10^{-4} = 1 \times 10^{-3} \, \text{Weber}
\]
\[
\Phi = 1 \times 10^{-3} \cdot \frac{1}{2} = 5 \times 10^{-4} \, \text{Weber}
\]
### Step 7: Convert Weber to Maxwell
To convert Weber to Maxwell, we use the conversion factor \(1 \, \text{Weber} = 10^8 \, \text{Maxwell}\):
\[
\Phi = 5 \times 10^{-4} \, \text{Weber} \times 10^8 \, \text{Maxwell/Weber} = 5 \times 10^4 \, \text{Maxwell}
\]
### Final Answer
The magnetic flux through the coil is:
\[
\Phi = 5 \times 10^4 \, \text{Maxwell}
\]
