Question

A toroidal core of relative permeability ?? = 3000, has a mean radius R = 80 mm and a circular cross section with radius b = 25 mm. An airgap ?? = 3 mm exists, and a current I flows in a 500-turn winding to produce a magnetic flux of 10−5 Wb, as shown in Figure Q2(a). Neglecting flux leakage and using mean path length, find:

1. The reluctances of the air gap and the iron core

2. ?? and ?? in the air gap and ?? and ?? in the iron core.

3. Say this toroid is to be used in an application as a linear Hall-effect sensor integrated circuit (IC) as shown in Figure Q2 (b), as a non-intrusive sensor to detect high current level in power electronic circuit. If the sensor is subjected to a high temperature (80oC) environment, how do you think the performance of toroid will be affected?

4. Determine the expression for the inductance per unit length of a very long solenoid with air core having N turns per unit length.

Answer 1

1. Reluctance:

  

  

  

  

  

2.  

So,

  

  

4. Inductance of solenoid

net flux =

magnetic filed, B, of a solenoid   

So,

So

For ques3 figure is not given.