Question

Find the flux (in T⋅m² ) of Earth's magnetic field of magnitude Bₑ =5.00×10⁻⁵

T through a circular loop of radius r=24.3 cm when the field is parallelto the normal to the plane of the loop.

Answer 1

The magnetic flux through a circular loop with Earth's magnetic field parallel to the normal of the loop's plane is approximately 9.25×10-5 T·m2.

Step-by-step explanation:

To calculate the magnetic flux through a circular loop when the Earth's magnetic field is parallel to the normal to the plane of the loop, we use the formula:

Φ = B · A · cos(θ)

where:

• Φ is the magnetic flux,
• B is the magnetic field's magnitude,
• A is the area of the loop, and
• cos(θ) indicates the angle between the magnetic field and the normal to the plane, which is 0 degrees since they are parallel.

Given:

• Be = 5.00×10−5 T (Earth's magnetic field magnitude), and
• r = 24.3 cm = 0.243 m (radius of loop).

We'll first calculate the area (A) of the circular loop:

A = π·r2

A = π·(0.243 m)2

A ≈ 0.185 m2

Now, since the field is parallel to the normal, cos(θ) is cos(0°) = 1.

Thus, the magnetic flux (Φ) can be calculated as:

Φ = (5.00×10−5 T) · (0.185 m2) · 1

Φ ≈ 9.25×10−5 T·m2

The approximate magnetic flux through the circular loop is 9.25×10−5 T·m2.