Final answer:
To calculate the magnitude of the flux through the square surface, use the formula Φ = B · A, where Φ is the flux, B is the magnetic field, and A is the area of the surface. In this case, the magnetic field is given as B = (0.225T)i + (0.325T)j − (0.500T)k, and the area is a square with side length 3.00 cm.
Step-by-step explanation:
To calculate the magnitude of the flux through the square surface, we can use the formula for magnetic flux: Φ = B · A, where Φ is the flux, B is the magnetic field, and A is the area of the surface. In this case, the magnetic field is given as B = (0.225T)i + (0.325T)j − (0.500T)k, and the area is a square with side length 3.00 cm. Since the surface is in the xy-plane at z=0, the k-component of the magnetic field does not contribute to the flux. Therefore, we only need to consider the magnetic field components in the xy-plane.
Let's calculate the magnitude of the magnetic field in the xy-plane:
Bxy = √(Bx² + By²) = √((0.225T)² + (0.325T)²) = √(0.050625T² + 0.105625T²) = √0.15625T² = 0.395T
Now, let's calculate the magnitude of the flux:
Φ = Bxy · A = (0.395T) · (0.03m)² = 0.395T · 0.0009m² = 0.000356 T·m²