What is the magnetic flux through the square due to this field?

Question

A 2m long metal wire is formed into a square and placed in the horizontal xy-plane. A uniform magnetic field is oriented at 30° above the horizontal with strength of 0.344 T. What is the magnetic flux through the square due to this field?

Answer 1

Where to start:

Identify the question: magnetic flux = Φ?

Identify the formula for magnetic flux: Φ = B · A · cosθ

Φ = magnetic flux units: Wb or T/m²

B = magnetic field units: T

A = Area units: m²

θ = angle

Identify what's given:

B = 0.344 T

A = (0.5)² = 0.25 m²

since the 2m wire is formed into a square, each side is 0.5m. Area of a square = (s)²

θ = 90 - 30 = 60°

Need the angle between the magnetic field and the normal to the loop

Plug into the formula:

Φ = (0.344)(0.25)cos(60) = 0.043 Wb

ANSWER: Φ = 0.043 Wb