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# Electro Magnetic Induction: Motional EMF in a satellite

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A natural satellite whose diameter is 10^4 meters moves at velocity of 1 km/s in the direction normal to the magnetic field of a planet in a region where B=10^-7 tesla. The satellite has appreciable conductivity.

A) The satellite moves in a perfect vacuum. What happens?

B) The ambient gas has a density of the order 10^10 particles per cubic meter, the particles being either electrons or singly charged ions. Each half of the satellite collects particles of the correct sign in sweeping thru space. Calculate the order of magnitude of the current.

C) Calculate the order of magnitude of the braking force.

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a natural satellite whose diameter is 10^4 meters moves at velocity of 1 km/s in the direction normal to the magnetic field of a planet in a region where B=10^-7 tesla. the satellite has appreciable conductivity.

A) the satellite moves in a perfect vacuum. what happens?

Let the satellite moves to the right and the field is coming out of the page. Like a conductor moves perpendicular to the field an EMF is induced in the satellite. If we consider the upright diameter (shown in the figure) the motional EMF induced across it will be given by

As the velocity of the satellite is perpendicular to the field and both are perpendicular to this diameter the magnitude of the induced EMF across this diameter will be

And the direction of this EMF is such that the top end of the diameter will be at lower potential.
As this distance is maximum perpendicular to field and velocity, the induced EMF is maximum. For rest of the vertical distances the EMF will be less and zero at the points on the circle parallel to velocity vector.
As no any closed loop is formed for which a net EMF will be nonzero, there will be no current anywhere. This EMF is utilized to keep the extraneous charges at their positions and a potential difference will be there between the upper and lower portions

B) the ambient gas has a density of the order 10^10 particles per cubic meter, the particles being either electrons or singly charged ions. each half of the satellite collects particles of the correct sign in sweeping thru space. calculate the order of magnitude of the current.
As the satellite moves through the charged particles, the upper hemisphere which is at lower potential will capture the positively charged ions and the lower will capture the electrons. As the satellite is a good conductor all the particles captured will be transferred due to induced EMF and there will be a current from upper part to the lower part.
Now projection of the area crossed by the two hemispheres normal to the direction of velocity will be the two semicircular area of radius D/2 each.
Thus the volume of the ambient gas swiped by upper hemisphere in time dt is given by

Thus the positive charge captured by the upper hemisphere will be

Here is the density of the particles and ½ because the electrons will not be captured by this part.
Hence the current between the two hemispheres due to the capture of positive ions by the upper hemisphere will be

Similarly the same current will be there due to capture of negatively charged electrons at the lower hemisphere and thus the total current between the two hemi sphere will be

Substituting the values we get

Thus the current in the satellite is of the order of 1020 A.

C) calculate the order of magnitude of the braking force.
Taking the average length of this conductor roughly as half of the diameter, the magnitude of breaking force (remember Lenz law) experienced by the satellite is given by

Or F = 10-7*3.9*1020*0.5*104 = 2.0*1017 N
Hence the force on the satellite is of the order of 1017 N.

Here we have to give order of the quantities, no complicated calculations are required.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

© BrainMass Inc. brainmass.com September 27, 2022, 5:14 pm ad1c9bdddf>
https://brainmass.com/physics/emf/electro-magnetic-induction-motional-emf-satellite-300563