Final answer:
To find the magnitude of the net magnetic field at the common center of the two circular loops, we can use Ampere's Law. Ampere's Law states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.
Step-by-step explanation:
To find the magnitude of the net magnetic field at the common center of the two circular loops, we can use Ampere's Law. Ampere's Law states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire. In this case, we have two loops of wire, each carrying a current of 2.50 A and having a radius of 5.10 cm. The net magnetic field at the common center can be calculated by summing the magnetic fields due to each loop.
Let's assume that the common center lies on the z-axis. The magnetic field at the common center due to each loop can be calculated using the equation:
B = (μ₀I)/(2R)
where B is the magnetic field, μ₀ is the permeability of free space (4π×10^-7 Tm/A), I is the current, and R is the radius of the loop.
Substituting the given values into the equation:
Magnetic field due to each loop:
B = (4π×10^-7 Tm/A)(2.50 A)/(2(0.051 m))
Net magnetic field at the common center:
B_total = 2B
Calculating the magnetic field due to each loop:
B = 2.47 × 10^-5 T
Calculating the net magnetic field at the common center:
B_total = 2(2.47 × 10^-5 T) = 4.94 × 10^-5 T