The induced emf between the ends of a wire segment moving parallel to a current-carrying wire is found by calculating the magnetic field strength at the wire segment and using the formula emf = Blv, where B is the magnetic field strength, l is the length of the wire segment, and v is its velocity.
To determine the induced emf (voltage) between the two ends of the wire segment, we can use the concept of motional emf in physics, which is given by the formula emf = Blv, where B is the magnetic field strength, l is the length of the wire, and v is the velocity of the wire segment perpendicular to the magnetic field. However, the magnetic field strength is not directly provided; it has to be calculated using Ampère's Law for a long straight wire, which states that B = (μ0 I) / (2π r), where μ0 is the permeability of free space (4π × 10-7 T·m/A), I is the current in the wire, and r is the distance from the wire to the point of interest.
After calculating the magnetic field strength, B, we can plug in the values along with the length of the wire segment, l = 5.1 cm or 0.051 m, and its velocity, v = 5.42 m/s, into the motional emf equation to find the induced emf.
Using the formula for B and substituting the given values (I = 6.70 A and r = 5.1 cm or 0.051 m), we find that B = (4π × 10-7 T·m/A × 6.70 A) / (2π × 0.051 m). Once we have the value for B, we calculate the induced emf using the formula emf = Blv.