How much thermal energy is produced in the loop? - magnetic loop antenna this is the
I'm not sure on how to integrate time into the equations of thermal energy. I was always 6.0755E-7, but that seems wrong.
An antenna loop of 2.00 cm ^ 2 and the resistance to 5.06 μOhms perpendicular to a homogeneous magnetic field of magnitude 20.0 to this value. The scale range is reduced to 2.40 ms zero. How much heat energy is in the circuit by generating the box?
Saturday, December 12, 2009
Magnetic Loop Antenna This Is The How Much Thermal Energy Is Produced In The Loop?
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2 comments:
I hope the following helps, but I'm a bit rusty in the theory.
If a change in the magnetic field induces current in a loop, we work with the Faraday's law, which states
The electromotive force (EMF) = - (change of magnetic flux) / time ()
The magnetic flux of the magnetic field area = x
= (20 x 10 ^ -6) x 2,99 x 10 ^ -4
= 59.8 x 10 ^ -10
EMC = (59.8 x 10 ^ -10) / (2.4 x 10 ^ -3) = 24.92 x 10 ^ -7 V
Power = V ^ 2 / R = (24.92x10 ^ -7) ^ 2 / (5.06x10 ^ -6)
= 122.72 x 10 ^ -8
Energy = Power x Time = 122.72 x 10 ^ -8 x 2.4 x 10-3
= 2.95 x 10 ^ -9
When the magnetic field drops to zero, the changing magnetic flux induces a current in the loop of wire. It is managed in Faraday law: E = df / dt, where E is the induced emf (in volts), F is the magnetic flux t is the time.
So, first calculate the magnetic flux through the coil, the B * A, where B is the magnetic field and A is the area of the loop. Thus, the flow (Weber 2.00cm ^ 2) * (20x10 ^-6T) = 4x10 ^ -9.
The flow of drops of 4x10 ^ -9 to 0 2.4x10 ^ -3 seconds, so that the induced EMF (4x10 ^ -9) / 2.4x10 ^ -3 = 1.67x10 ^ -6 V.
This leads to an induced voltage = current, which can be calculated with V = I * R I = (1.67x10 ^-6V) / (5.06x10 ^ -6 ohms) 0.33 amps.
The thermal energy produced is exactly equal to the power dissipated by the current and resistance in the loop. The formula for power is P = I * R ^ 2, (5.06x10 ^ -6 ohms) * (0.33 amps) ^ 2 = 5.5x10 ^ 7 watts, which is pretty close to what you already have!
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