19/10/2020 Part 1A - Electromagnetics Cambridge University Engineering Department Michaelmas Term 2020 Prof. T. D. Wilkinson (tdw13@cam.ac.uk) Handout I - The physical principles of electronics (PPE) ( And now, the gap is near, and so I face, the final curtain ... ) 1 Magnetic flux density on axis of a wire loop More geometry ... The current carrying wire loop is the basis of more complex engineering structures, such as the solenoid. We consider the calculation of the magnetic field at a point P on the axis of the loop and height z above carrying a current I. 2 1
19/10/2020 B is axial only r z a a I B/S law H?I 4Tr2 x 2?? x cos a Axial B only Integrate around loop a cos a = - B = u Ia2 r = Va2 + z2 )3/2 r 2 (a2 +z2) 3 Magnetic flux density inside a solenoid Lots of loops The solenoid, and related devices, is commonly used to produce magnetic fields. We shall make use of the results of our previous example and consider the solenoid to be made up of many closely spaced loops, each carrying current I. By Zureks - Own work, Public Domain, https://commons.wikimedia.org 4 2
19/10/2020 Read carefully The solenoid has N turns/unit length, so that in a short length oz there are Noz loops. Then we use our previous result to write down the B field produced on axis by the section Sz. The total field is given by integrating over all these elements along the z axis. For simplicity, we assume the solenoid is infinitely long, although the case of finite length is easily calculated from our analysis. 5 Infinitely long a B N turns/unit length Infinitely long B I 0 Z Sz From 1 loop ex: we now have N& loops 2 0 SB = N Sz 2\a+ + z2 13/2 Integrate along z HoINa2 . +00 1 dz B = 3/2 2 -001 la2 + z2) Sub z = a tan a I = LONI 6 3