10. A circular coil of diameter 20 mm is mounted with the plane of coil perpendicular to the direction flux density of 100 mT. Find the total flux passing through.

A. 45.6 μWb
B. 52.1 μWb
C. 38.2 μWb
D. 31.4 μWb

Question

High School

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Answer :

JessicaJessy JessicaJessy · Answer 1 · 2024-01-18T11:58:14-05:00

To find the total magnetic flux passing through the circular coil, we need to use the formula for magnetic flux (Φ), which is given by:

[tex]Φ = B \cdot A \cdot \cos(θ)[/tex]

where:

[tex]B[/tex] is the magnetic flux density (in Tesla), which is given as 100 mT or 0.1 T.
[tex]A[/tex] is the area of the coil (in square meters).
[tex]θ[/tex] is the angle between the magnetic field and the normal to the plane of the coil. Since the coil is mounted perpendicular to the magnetic field, [tex]θ = 0[/tex] degrees, and [tex]\cos(0) = 1[/tex].

First, calculate the area [tex]A[/tex] of the coil. The area of a circle is given by:

[tex]A = \pi \left(\frac{d}{2}\right)^2[/tex]

where [tex]d[/tex] is the diameter of the coil. Convert the diameter from millimeters to meters:

[tex]d = 20 \text{ mm} = 0.02 \text{ m}[/tex]

Now calculate the radius [tex]r[/tex] and the area [tex]A[/tex]:

[tex]r = \frac{0.02}{2} = 0.01 \text{ m}[/tex]

[tex]A = \pi (0.01)^2[/tex]

[tex]A \approx \pi \times 0.0001[/tex]

[tex]A \approx 0.000314 \text{ m}^2[/tex]

Now calculate the magnetic flux [tex]Φ[/tex]:

[tex]Φ = 0.1 \times 0.000314 \times 1[/tex]

[tex]Φ = 0.0000314 \text{ Wb}[/tex]

Convert Weber to micro Weber (1 Wb = 1,000,000 μWb):

[tex]Φ = 31.4 μWb[/tex]

Thus, the total flux passing through the coil is 31.4 μWb, which corresponds to option D.