Question

Two perpendicular straight wires join in the ends of semicircular loop of radius a = 12 cm_ as shown in the figure above. If the current [ = I0A= what is the resultant field at the center of the circular section?

T out of the page.

Answer 1

The resultant magnetic field at the center of a semicircular loop with a perpendicular current is half the magnitude of the field at the center of a full circle and is directed out of the page.

Step-by-step explanation:

The question at hand involves determining the magnetic field at the center of a semicircular loop connected to two perpendicular straight wires, all carrying a constant current I. To find the resultant field at the center of the circular section, you use the Biot-Savart Law or Ampere's law. The field due to the straight wires at the center of the loop is zero because the wires are perpendicular to the radius vector of the loop's center. However, for a full circular loop, the field at the center is given by B = μ0I / (2R), where μ0 is the permeability of free space, I is the current, and R is the radius. Since we have only a half-circle, the field's magnitude will be half of this value and directed perpendicularly out of the page (following the right-hand rule).

To summarize, the resultant magnetic field at the center of the semicircular loop of radius a with current I is B = μ0I / (4a), pointing out of the page.