A square coil of side 30cm with 500 turns is kept in a uniform magnetic field of 0.4T. the plane of the coil is inclined at an angle of 30° to the field. Calculate the magnetic flux through the coil.
To calculate the magnetic flux through the coil, we need to use the formula:
Φ = B * A * cos(θ),
where:
Φ is the magnetic flux,
B is the magnetic field strength,
A is the area of the coil, and
θ is the angle between the magnetic field and the plane of the coil.
Let's find the values step by step:
1. Calculate the area of the coil:
Given that the coil is a square with a side length of 30 cm, we can calculate its area using the formula:
A = side^2,
A = 30 cm * 30 cm = 900 cm^2.
2. Convert the area to square meters:
Since the SI unit of area is square meters, we need to convert the area from cm^2 to m^2:
A = 900 cm^2 * (1 m^2 / 10,000 cm^2) = 0.09 m^2.
3. Calculate the cosine of the angle:
The angle between the magnetic field and the plane of the coil is given as 30°. We need to convert this angle to radians before calculating the cosine:
θ (in radians) = 30° * (π / 180°) ≈ 0.524 rad.
4. Calculate the magnetic flux:
Using the formula Φ = B * A * cos(θ):
Φ = 0.4 T * 0.09 m^2 * cos(0.524 rad) ≈ 0.0342 Wb.
Therefore, the magnetic flux through the coil is approximately 0.0342 Weber (Wb).