Question

A circular loop of radius 12.3 cm is placed in a uniform magnetic field. If the field is directed perpendicular to the plane of the loop and the magnetic flux through the loop is 7.70 x 10⁻³ T. m²a, what is the st ength of the magnetic feld?

Answer 1

To find the magnetic field strength in a circular loop, the magnetic flux is divided by the area of the loop. Given the flux and radius, one can calculate the strength using the formula B = Φ/(πr²).

Step-by-step explanation:

The question revolves around the concept of magnetic flux through a circular loop and the magnetic field strength. Magnetic flux (Φ) can be defined as the product of the magnetic field (B), the area it penetrates (A), and the cosine of the angle (θ) between the magnetic field direction and the normal to the plane of the loop. In this case, since the magnetic field is directed perpendicular to the plane of the loop, cos(θ) is 1, and the formula for magnetic flux simplifies to Φ = BA. To find the magnetic field strength, we use the formula rearranged as B = Φ/A.

Given that the magnetic flux through the loop Φ is 7.70 x 10−3 T·m² and the radius of the loop r is 12.3 cm (or 0.123 m), we can calculate the area of the loop A using the formula A = πr². Then we can solve for B:

A = π(0.123 m)²

B = Φ / A

By substituting the given values into these equations, we can determine the magnetic field strength B.