If a magnetic field of 0.1 T is perpendicular to a circular loop of radius 0.1 m, what is the magnetic flux through the loop?

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Q: If a magnetic field of 0.1 T is perpendicular to a circular loop of radius 0.1 m, what is the magnetic flux through the loop?

Solution: Magnetic flux (Φ) = B * A = B * πr². Here, A = π(0.1)² = 0.01π m². Thus, Φ = 0.1 * 0.01π = 0.01π Wb ≈ 0.0314 Wb.

Steps: 10

Step 1: Identify the magnetic field strength (B). In this case, B = 0.1 T (Tesla).
Step 2: Identify the radius of the circular loop (r). Here, r = 0.1 m.
Step 3: Calculate the area (A) of the circular loop using the formula A = πr².
Step 4: Substitute the radius into the area formula: A = π(0.1)².
Step 5: Calculate (0.1)², which is 0.01. So, A = π * 0.01.
Step 6: Now, calculate the area: A = 0.01π m².
Step 7: Use the formula for magnetic flux (Φ): Φ = B * A.
Step 8: Substitute the values of B and A into the flux formula: Φ = 0.1 * 0.01π.
Step 9: Calculate the magnetic flux: Φ = 0.001π Wb.
Step 10: To get a numerical value, calculate 0.001 * π, which is approximately 0.00314 Wb.