Two flat surfaces are exposed to a uniform, horizontal magnetic field of magnitude 0.79 T. When viewed edge-on, the first surface is tilted at an angle of 26° from the horizontal, and a net magnetic flux of 9.2 x 10-4 Wb passes through it. The same net magnetic flux passes through the second surface. (a) Determine the area of the first surface. (b) Find the smallest possible value of the area of the second surface.

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To solve this problem, we can use the equation for magnetic flux:

Φ = B * A * cos(θ)

Where Φ is the magnetic flux, B is the magnetic field, A is the area, and θ is the angle between the magnetic field and the area vector.

(a) To determine the area of the first surface, we can rearrange the equation:

A = Φ / (B * cos(θ))

Plugging in the given values:

Φ = 9.2 x 10^(-4) Wb
B = 0.79 T
θ = 26°

A = (9.2 x 10^(-4)) / (0.79 * cos(26°))

Using a scientific calculator, calculate the cosine of 26°:

cos(26°) ≈ 0.8944

A ≈ (9.2 x 10^(-4)) / (0.79 * 0.8944)

A ≈ 0.0011603 m^2

Therefore, the area of the first surface is approximately 0.0011603 square meters.

(b) To find the smallest possible value of the area of the second surface, we know that the same net magnetic flux passes through it. Therefore, we can use the same equation:

A = Φ / (B * cos(θ))

Plugging in the given values:

Φ = 9.2 x 10^(-4) Wb
B = 0.79 T
θ = 0° (since the second surface is tilted edge-on, the angle is 0°)

A = (9.2 x 10^(-4)) / (0.79 * cos(0°))

Using a scientific calculator, calculate the cosine of 0°:

cos(0°) = 1

A = (9.2 x 10^(-4)) / (0.79 * 1)

A ≈ 0.0011646 m^2

Therefore, the smallest possible value of the area of the second surface is approximately 0.0011646 square meters.

To solve this problem, we can use the formula for magnetic flux:

Φ = B * A * cosθ

Where:
Φ is the magnetic flux
B is the magnetic field strength
A is the area
θ is the angle between the magnetic field and the normal vector of the surface.

For the first surface, we are given:
Φ₁ = 9.2 x 10^(-4) Wb (given)
B = 0.79 T (given)
θ₁ = 26°

Now we can rearrange the formula to solve for the area A₁ of the first surface:

A₁ = Φ₁ / (B * cosθ₁)

Substituting the given values:
A₁ = (9.2 x 10^(-4) Wb) / (0.79 T * cos(26°))

Calculating this equation will give us the area of the first surface (A₁).

Moving on to the second part, we need to find the smallest possible value of the area of the second surface (A₂). We know that the same net magnetic flux passes through this surface, so we can set up the following equation:

Φ₂ = Φ₁

Using the formula for magnetic flux and rearranging it to solve for the area A₂:

Φ₂ = B * A₂ * cosθ₂

A₂ = Φ₂ / (B * cosθ₂)

Since we want to find the smallest possible value of A₂, we need to find the maximum value of cosθ₂. The maximum value of cosθ₂ is 1, which occurs when θ₂ = 0°.

Therefore, the smallest possible value of A₂ can be found as:

A₂ = Φ₂ / B

Using Φ₂ = Φ₁, we can substitute and calculate A₂.

By solving these equations, we can find the area of the first surface (A₁) and the smallest possible value of the area of the second surface (A₂).