Question

A horizontal rectangular surface has dimensions 3.25 cm by 3.85 cm and is in a uniform magnetic field that is directed at an angle of 29.0 ∘ above the horizontal. What must the magnitude of the magnetic field be to produce a flux of 3.80×10⁻⁴ Wb through the surface?

Answer 1

The magnitude of the magnetic field required to produce a flux of 3.80×10⁻´ Wb through a surface of 3.25 cm by 3.85 cm is approximately 3.47×10⁻² T.

Step-by-step explanation:

To calculate the required magnitude of the magnetic field that produces a magnetic flux of 3.80×10⁴ Wb through a surface, we use the formula for magnetic flux Φ = B⋅A⋅cosθ, where B is the magnetic field strength, A is the area through which the field lines pass, and θ is the angle between the field lines and the normal to the surface. First, we need to calculate the area of the rectangle which is 3.25 cm by 3.85 cm.

A = length × width = (3.25 cm) × (3.85 cm) = 12.5125 cm² = 1.25125×10⁻² m²

To find the magnetic field strength, we rearrange the formula to B = Φ / (A⋅cosθ). The angle θ is given as 29.0 degrees above the horizontal.

Now we can plug in the values:

• Φ = 3.80×10⁻´ Wb
• A = 1.25125×10⁻² m²
• θ = 29.0°

Then,

cosθ = cos(29.0°) = 0.8746

Thus, B = (3.80×10⁻´ Wb) / (1.25125×10⁻² m² ⋅ 0.8746)

So, B ≈ 3.80×10⁻´ Wb / 1.09466×10⁻² = 3.47×10⁻² T (Teslas)

The magnitude of the magnetic field required is approximately 3.47×10⁻² T.