A L=3 mile long conducting cable tethers a satellite to the International Space Station. The Cable moves through the Earth' magnetic field of about B=0.02 Gauss at a speed of v=8 km/sec. The cable points radially from the Space Station to the satellite. The ISS moves Eastwards and the magnetic field is Northward.
What is the potential difference between the two ends of the tether ?
1T=10000 Gauss
B=0.02•10⁻⁴= 2•10⁻⁶ T
v=8 km/s=8•10³ m/s
U=BLv= 2•10⁻⁶•4828• 8•10³=77.25 V
thnx :)
To calculate the potential difference between the two ends of the tether, we need to use the formula for induced emf (electromotive force) caused by the motion of the cable through the Earth's magnetic field. The formula is:
emf = B * L * v
Where:
- emf is the induced electromotive force (potential difference)
- B is the magnetic field strength
- L is the length of the cable
- v is the velocity of the cable moving through the magnetic field
In this case, we have:
B = 0.02 Gauss (convert to Tesla: 1 Gauss = 10^-4 Tesla)
L = 3 miles (convert to meters: 1 mile = 1609 meters)
v = 8 km/sec (convert to meters/sec: 1 km = 1000 meters)
Let's convert the given values into the appropriate units first:
B = 0.02 Gauss = 0.02 * 10^-4 Tesla = 2 * 10^-6 Tesla
L = 3 miles = 3 * 1609 meters = 4827 meters
v = 8 km/sec = 8 * 1000 meters/sec = 8000 meters/sec
Now we can substitute these values into the formula:
emf = (2 * 10^-6 Tesla) * (4827 meters) * (8000 meters/sec)
Calculating this, we find:
emf ≈ 0.07728 volts
Therefore, the potential difference between the two ends of the tether is approximately 0.07728 volts.