1. Electromagnetism Lecture#16-17 Instructor: Muhammad Mateen Yaqoob

2. Magnetic Field Created by an Infinite Current Sheet Mateen Yaqoob Department of Computer Science

3. Magnetic Field Created by an Infinite Current Sheet Mateen Yaqoob Department of Computer Science

4. Magnetic Field Created by an Infinite Current Sheet Mateen Yaqoob Department of Computer Science

5. The Magnetic Field of a Solenoid  Solenoid is a long wire wound in form of a helix. With this configuration, a reasonably uniform magnetic field can be produced in space surrounded by turns of wire, when solenoid carries a current. When turns are closely spaced, each can be approximated as a circular loop, and net magnetic field is vector sum of fields resulting from all turns. Mateen Yaqoob Department of Computer Science

6. The Magnetic Field of a Solenoid  Note that field lines in interior are nearly parallel to one another, are uniformly distributed, and are close together, indicating that field in this space is strong and almost uniform.  If turns are closely spaced and solenoid is of finite length, magnetic field lines are shown in figure. This field line distribution is similar to that surrounding a bar magnet. Hence, one end of solenoid behaves like north pole of a magnet, and opposite end behaves like south pole. As length of solenoid increases, interior field becomes more uniform and exterior field becomes weaker.  An ideal solenoid is approached when turns are closely spaced and length is much greater than radius of turns. Mateen Yaqoob Department of Computer Science

7. Ideal Solenoid  Figure shows a longitudinal cross section of part of such a solenoid carrying a current I. In this case, external field is close to zero, and interior field is uniform over a great volume.  If we consider an Amperian loop perpendicular to page in, surrounding ideal solenoid, we see that it encloses a small current as charges in wire move coil by coil along length of solenoid.  Contribution along side 3 is zero because magnetic field lines are perpendicular to path in this region. Contributions from sides 2 and 4 are both zero, again because B is perpendicular to ds along these paths, both inside and outside solenoid. Side 1 gives a contribution to integral because along this path B is uniform and parallel to ds. Integral over closed rectangular path is therefore Mateen Yaqoob Department of Computer Science

8. Gauss’s Law in Magnetism  Earlier we found that electric flux through a closed surface surrounding a net charge is proportional to that charge (Gauss’s law). In other words, number of electric field lines leaving surface depends only on net charge within it. This property is based on fact that electric field lines originate and terminate on electric charges.  Situation is quite different for magnetic fields, which are continuous and form closed loops. In other words, magnetic field lines do not begin or end at any point. Gauss’s law in magnetism states that “net magnetic flux through any closed surface is always zero”.  This statement is based on experimental fact, that isolated magnetic poles (monopoles) have never been detected and perhaps do not exist. Nonetheless, scientists continue search because certain theories that are otherwise successful in explaining fundamental physical behavior suggest possible existence of monopoles. Mateen Yaqoob Department of Computer Science