Consider a conducting ring of radius a and resistance R. part a Case I We first place the ring in a constant magnetic field B = B0 pointing into the page as shown in Figure 9. part b Case II Next, we place the ring from part a in a time-varying magnetic field given by B = B0(1 −t/T) 0 < t ≤ T a) Calculate the induced emf in the loop. b) Calculate the magnitude of the induced current in the ring. c) State the direction of the induced current in the ring. Sketch the current and justify your answer.
Ampere Circuital Law
Ampere's Law states that "for any closed loop path, the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop.”
Current Density
To design the electrical and electronic system, the current density is an important factor. The designer current level is the factor on which the circuit performance depends and with the help of the dimensions of the conducting current the current density is then determined. For instance, despite the lower current demanded by smaller devices as integrated circuits are reduced in size, there is a type of trend in achieving the higher device number in even smaller chip areas. The current density is increased in this region at higher frequencies because the conducting region in a wire becomes confined and this is known as the skin effect. The consequences increase as the current densities become higher.
Consider a conducting ring of radius a and resistance R.
part a
Case I We first place the ring in a constant magnetic field B = B0 pointing into the page as
shown in Figure 9.
part b
Case II Next, we place the ring from part a in a time-varying magnetic field given by
B = B0(1 −t/T)
0 < t ≤ T
a) Calculate the induced emf in the loop.
b) Calculate the magnitude of the induced current in the ring.
c) State the direction of the induced current in the ring. Sketch the current and justify your
answer.
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