Final answer:
The magnetic field in the region where the Hall probe reading is 2.68 μV for 1.57 A of current is approximately 2.15 T, based on the proportionality of Hall voltage to both magnetic field strength and current.
Step-by-step explanation:
The question is about determining the magnetic field in a region based on a reading from a Hall probe for a different current than the one in the initial measurement. The Hall probe gives us a way to measure magnetic fields by outputting a voltage that's proportional to both the field strength and the current passed through the probe.
In the case provided, the first relationships we have are 1.72 μV for 2.41 A in a 1.31 T field. The second reading we have is 2.68 μV for 1.57 A, and we need to find the magnetic field in Tesla (T) for this second reading. Since the output voltage of a Hall probe is directly proportional to both the magnetic field and the current flowing through it, we can express the relationship as V1/I1*B1 = V2/I2*B2. This allows us to solve for the magnetic field in the second region, B2.
The calculation is as follows:
V1/I1*B1 = V2/I2*B2
(1.72 μV / 2.41 A) * 1.31 T = (2.68 μV / 1.57 A) * B2
B2 = [(1.72 μV / 2.41 A) * 1.31 T] / (2.68 μV / 1.57 A)
B2 = (1.72 * 1.31 / 2.41) / (2.68 / 1.57) T
B2 ≈ 2.1548 T
Therefore, the magnetic field in the region where the reading is 2.68 μV for 1.57 A of current is approximately 2.15 T.