a satellite orbitting the earth at the equator at a na ltitude of 400 km, has an antenna that can be modelled as a 2.0m long rod. the antenna is oriented perpndicular to the earth's surface. at the equator, the earth's magnetic field is essentially horizontal and has a value of 8.0*10^-5 t;ignore any change in B with altitude. assuming the orbit is circular, determine the induced emf between the tips of the antenna.
Compute the orbital speed V at that altitude, in m/s. It should be several thousand m/s. You can get it by equating the centripetal force to the gravity force. You will need the earth's radius.
Charge q in the rod experiences a force B*V*q. Along length L, there will be a voltage difference B*V*L.
B is the mag. field in Tesla and L is the antenna length in meters.
To determine the induced EMF (electromotive force) between the tips of the antenna, we need to apply Faraday's law of electromagnetic induction. According to Faraday's law, the induced EMF can be calculated by multiplying the rate of change of magnetic flux through the loop of the antenna by the number of turns in the loop.
In this case, the antenna can be modeled as a 2.0m long rod, so the length of the loop is 2.0m. The induced EMF will be generated due to the change in the magnetic flux as the satellite moves through the Earth's magnetic field.
To calculate the induced EMF, we need to determine the change in magnetic flux through the loop. The magnetic flux through a loop can be calculated by multiplying the magnetic field strength by the area of the loop.
Since the antenna is perpendicular to the Earth's surface, the area of the loop is given by the length of the loop multiplied by the width (which can be assumed to be 1m since the antenna is a rod).
Therefore, the area of the loop is 2.0m * 1m = 2.0m².
The change in magnetic flux can be found by subtracting the initial magnetic flux from the final magnetic flux as the satellite moves through the Earth's magnetic field. In this case, the magnetic field is essentially horizontal and has a value of 8.0*10^-5 Tesla (T).
Since the altitude is given as 400km, we can ignore any change in the magnetic field with altitude.
The initial magnetic flux is zero because the satellite is not in the Earth's magnetic field initially. The final magnetic flux is given by multiplying the magnetic field strength by the area of the loop.
Therefore, the change in magnetic flux is (8.0*10^-5 T) * (2.0m²) = 1.6*10^-4 T·m².
Now, we can calculate the induced EMF by multiplying the rate of change of magnetic flux by the number of turns in the loop. In this case, since the antenna is a simple rod, we can assume it has only one turn.
Hence, the induced EMF is (1.6*10^-4 T·m²) * 1 = 1.6*10^-4 V (or volts).
Therefore, the induced EMF between the tips of the antenna is 1.6*10^-4 volts.