Final answer:
To calculate the motional emf, use the formula emf = B * l * v * sin(θ) with B as the magnetic field, l as the length of the conductor, v as the velocity, and θ as the angle between velocity and magnetic field. Given values lead to an emf of 7.8 V.
Step-by-step explanation:
To calculate the motional emf induced in a conductor moving through a magnetic field, we need to use the equation emf = B * l * v * sin(θ), where B is the magnetic field strength, l is the length of the conductor, v is the velocity, and θ is the angle between the velocity and the magnetic field.
In the given problem, we have:
- B = 5.00 x 10-5 T (the Earth's magnetic field strength)
- l = 20.0 km = 20,000 m (the length of the conductor)
- v = 7.80 km/s = 7,800 m/s (the orbital speed)
- θ = 90 degrees (since the conductor is moving perpendicular to the magnetic field)
Because the conductor is moving perpendicular to the magnetic field, sin(θ) = sin(90°) = 1. Therefore, the emf induced is:
emf = B * l * v * sin(θ) = 5.00 x 10-5 T * 20,000 m * 7,800 m/s * 1 = 7.8 V