What is the force on a 1025 kg elevator that is falling freely at 9.8 m/sec 2?
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Hi there!
We can use Ampère's Law:
B = Magnetic field strength (B)
dl = differential length element (m)
μ₀ = Permeability of free space (T/Am)
Since this is a closed-loop integral, we must integrate over a closed loop. We can integrate over a rectangular-enclosed area of the rim of the solenoid - ABCD - where AD and BC are perpendicular to the solenoid.
Thus, the magnetic field is equivalent to:
Since AD and BC are perpendicular, and since:
If perpendicular to the field, the equation equals 0.
Additionally, since AB is outside of the solenoid, there is no magnetic field present, so B = 0. The only integral we integrate now is:
Which is horizontal and inside the solenoid. Let the distance between C and D be 'L', and the enclosed current is equivalent to the number of loops multiplied by the current:
N = # of loops per length multiplied by the length, so:
Plug in the given values and solve. Remember to convert # of loops to # of loops per unit length.