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Find the flux of Earth's magnetic field of magnitude $5.00 \times$ $10^{-5} \mathrm{T}$ through a square loop of area 20.0 $\mathrm{cm}^{2}(\mathrm{a})$ when the field is perpendicular to the plane of the loop, (b) when the field makes a $30.0^{\circ}$ angle with the normal to the plane of the loop, and (c) when the field makes a $90.0^{\circ}$ angle with the normal to the plane.

a. 10^{-3} \mathrm{T} \mathrm{cm}^{2}

b. 0.866 * 10^{-4} \mathrm{T} \mathrm{cm}^{2}

c. 0 \mathrm{T} \mathrm{cm}^{2}

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University of Washington

Hope College

University of Sheffield

McMaster University

our question wants us to find the flux of Earth's magnetic field, which is has a value be Will the five times send the minus five Tesla through a square loop of area a equal to 20 centimeter square, or 0.2 meters squared. So for party it wants us to find when the field is perpendicular to the plane. Emotion for part B, when it's 30 degrees to the plane in motion and see when the field is 90. Greece, uh, normal to the plate in motion. So for part A, we're gonna use the equation for magnetic flux, which is five b is equal to the magnetic field times the area Times Co. Sign times the coast sine of the angle Fada, and for our A fada is equal to zero degrees. Okay, so if you plug zero degrees in for data and that expression, as well as the value for the magnetic field in the area that we were given, we find that five B is equal to one times 10 to the minus seven, and the units here are Tesla Times meters squared. We can box set in. Draw that box, weaken box this inn is their solution for part A. Now, for part B, we're going to use the exact same expression for the magnetic flux, except for in part B. Fada, we're told, is equal to 30 degrees. So plugging in 30 degrees into the expression for the magnetic flux, we find that the magnetic flux here is equal to 8.66 times 10 to the minus eight and again units Tesla up times meters squared. We'll box set and as her solution for B and then lastly for part C for us to find the magnetic flux when the field makes a angle of 90 degrees normal to the plane. So now again, same expression for magnetic flux. But fatal here is equal to 90 degrees. So plugging 90 degrees in well, the coastline of 90 is equal to zero, and anything times zero is equal to zero. So the magnetic flux is just gonna be zero box. It in is their solution