The drawing shows two surfaces that have the same area. A uniform magnetic field B fills the space occupied by these surfaces and is oriented parallel to the yz plane as shown. If = 17°, find the ratio xz/ xy of the magnetic fluxes that pass through the surfaces.

90-17=73

(cos73)/(cos17)

I have no idea of the picture. Flux is B.Area, where . means dot product.

Well, well, we are getting a bit magnetic here! Let's unravel this puzzle, shall we?

First, let's imagine these surfaces, like two roommates, peacefully coexisting in the yz plane. Now, imagine a magnetic field B, parallel to this plane, playing the role of a mischievous cat trying to pass through the surfaces.

Now, we have this angle θ, or as I like to call it, the "I-don't-know-which-way-to-go" angle, at 17 degrees. This angle magically splits the magnetic field into two components, one along the surface xy and one along xz.

Now, let's compare the flux passing through these surfaces, shall we?

The flux through the surface xy is given by Φ(xy) = B * A * cos(θ), where A is the area of the surface. But wait! We forgot about the area of the parallel surfaces! No worries, though, because these surfaces have the same area, so we can just call it A.

Similarly, the flux through the surface xz is given by Φ(xz) = B * A * sin(θ). Now, let's combine these expressions and create a ratio, because ratios are like the 'cool' kids at school.

Therefore, the ratio xz/xy = (B * A * sin(θ)) / (B * A * cos(θ)) = sin(θ) / cos(θ).

And guess what? That's a trigonometric identity right there! Boom! sin(θ) / cos(θ) = tan(θ).

So, my friend, the ratio of the magnetic fluxes passing through these surfaces is simply tan(θ), where θ is 17 degrees. Now go forth and enjoy your magnetic adventures! 🌩️

To find the ratio xz/xy of the magnetic fluxes that pass through the surfaces, we need to use the concept of magnetic flux and apply it to each surface individually.

Magnetic flux is the quantity that measures the total magnetic field passing through a closed surface. The magnetic flux (Φ) passing through a surface is given by the equation:

Φ = B * A * cos(θ)

where B is the magnetic field strength, A is the area of the surface, and θ is the angle between the magnetic field lines and the surface normal.

Given that the magnetic field (B) is uniform and parallel to the yz plane, it means that the angle θ is the same for both surfaces since their orientations are the same. Thus, θ = 17° for both surfaces.

Now, let's denote the area of the first surface as A1 and the area of the second surface as A2. We know that both surfaces have the same area, so A1 = A2 = A.

For the first surface (xz plane), the magnetic flux (Φ1) passing through it is given by:

Φ1 = B * A * cos(θ)

For the second surface (xy plane), the magnetic flux (Φ2) passing through it is also given by:

Φ2 = B * A * cos(θ)

To find the ratio xz/xy, we need to divide the first flux by the second flux:

xz/xy = Φ1 / Φ2

Since Φ1 = Φ2, the ratio simplifies to:

xz/xy = 1

Therefore, the ratio xz/xy of the magnetic fluxes that pass to the surfaces is equal to 1.