RI Chap 17 Electromagnetic Forces Lecture Notes

17 ELECTROMAGNETIC FORCES H2 Physics 9478 Content Page 17.1 Concept of a Magnetic Field 2 17.2 Magnetic Fields Due to Currents 5 17.3 Force on a Current-Carrying Conductor 9 17.4 Forces Between Current-Carrying Conductors 15 17.5 Force on a Moving Charge 19 17.6 Motion of a Charged Particle in a Magnetic Field 20 17.7 Appendix 26 Learning Outcomes Candidates should be able to: (a) show an understanding that a magnetic field is an example of a field of force produced either by current carrying conductors or by permanent magnets (b) sketch magnetic field lines due to currents in a long straight wire, a flat circular coil, and a long solenoid (c) use 0 2B d µ π= I , 0 2 NB r µ= I and B = µ0nI for the magnetic flux densities of the fields due to currents in a long straight wire, a flat circular coil, and a long solenoid respectively [Not in H1 syllabus] (d) show an understanding that the magnetic field due to a solenoid may be influenced by the presence of a ferrous core [Not in H1 syllabus] (e) show an understanding that a current -carrying conductor placed in a magnetic field might experience a force (f) recall and solve problems using the equation sinF BIL θ= , with directions as interpreted by Fleming’s left-hand rule (g) define magnetic flux density as the force acting per unit current per unit length on a conductor placed perpendicular to the magnetic field (h) show an understanding of how the force on a current-carrying conductor can be used to measure the flux density of a magnetic field using a current balance (i) explain the forces between current-carrying conductors and predict the direction of the forces [not in H1 syllabus] (j) predict the direction of the force on a charge moving in a uniform magnetic field. (k) recall and solve problems using the equation sinF BQv θ= . (l) describe and analyse deflections of beams of charged particles by uniform electric fields and uniform magnetic fields. (m) explain how perpendicular electric and magnetic fields can be used in velocity selection for charged particles

Page | 2 17.1 Concept of a Magnetic Field  Properties of Magnets • Natural magnets were discovered from ancient archaeological sites more than two thousand years old. The term ‘magnet’ comes from the name of one of the locations these stones were found. • Experiments have shown that (i) magnetic poles are of two kinds, i.e. north (N) or south (S), (ii) like poles repel each other, unlike poles attract, (iii) poles occur only in opposite pairs (dipoles), (iv) when no other magnet is near, a freely suspended magnet will rotate so that the line joining its poles is approximately parallel to the Earth’s axis of rotation, and (v) the pole of the magnet that points towards the Earth’s Geomagnetic North is called the north pole of the magnet and the other the south pole of the magnet.  Magnetic Field • Forces between magnets can be explained using the concept of a magnetic field. o A magnet sets up a magnetic field in its vicinity. o The force exerted by one magnet on another magnet is due to the interaction between the magnetic fields set up by both magnets. • Quantitatively, the “strength” of a magnetic field is expressed by a quantity called the magnetic flux density (B). Its SI unit is the tesla (T). (The magnetic flux density and its unit will be defined later.) Magnetic flux density is a vector. • It is important to note that a moving charge placed in a magnetic field can experience a magnetic force when it is not moving parallel to the magnetic field. (Static charge placed in a magnetic field will not experience a magnetic force.) Note: There is a subtle difference between the following two terms: • magnetic flux density, denoted by symbol B (in syllabus). • magnetic field strength, denoted by symbol H, where B = µ0 H (not in syllabus). Definition 1 A magnetic field is a region of space in which a moving charge or a current -carrying conductor or a ferromagnetic object can experience a magnetic force when it is placed in the magnetic field. Hence, it is known as a field of force.

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page | 3  Representation of a Magnetic Field A magnetic field can be represented by field lines drawn such that • the tangent to a field line at a point gives the direction of B at that point, • the number of lines per unit cross −sectional area is an indicaton of the magnitude of B, i.e. if the lines are spaced closer, the magnitude of B is greater. If the field is uniform, the field lines are parallel and evenly spaced, and • the arrows point away from the north pole of a magnet to the south pole. This is because the direction of a field line is given by the direction of the force that acts on the north pole of a magnet. For a two-dimensional view, magnetic fields can be represented by dots or crosses, depending on whether it is perpendicularly pointing out of or into the plane of the paper, respectively.  Examples of Field Patterns Equally spaced parallel field lines ⇒ B is constant, i.e. a uniform field Field lines close together ⇒ B large Direction of B at P (tangential to P) P B small Fig. 17.1 Fig. 17.2 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x B out of page B into page Fig. 17.3 (b) U-shaped magnet N (a) Bar magnet N S

Page | 4  Earth’s Magnetic Field • The Earth’s magnetic field is a weak magnetic field believed to be caused by electric currents circulating within the core of the Earth. • The magnitude and direction of this field varies with position over the Earth’s surface and changes gradually with time. • The axis of the Earth’s magnetic field is tilted approximately 11 ° with respect to its rotational axis. Hence, the geographical North does not coincide exactly with the geomagnetic North. • The field pattern is similar to that of a bar magnet embedded deep inside the Earth as shown in Fig. 17.4. • From the field pattern, it is seen that near the equator, the Earth’s magnetic field, B Earth, is almost horizontal. • At all other positions, the BEarth is inclined at various angles (called the angle of dip, α ) from the horizontal. It is useful to resolve BEarth into horizontal and vertical components. BH = BEarth cos α BV = BEarth sin α Compass needles whose motion is confined in a horizontal plane are affected only by BH. S N Bv surface of Earth α BH BEarth geographical north geomagnetic North ~11° Fig. 17.4 α S N Geomagnetic North is actually a magnetic south pole (it attracts the N pole of a compass)

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page | 5 17.2 Magnetic Fields Due to Currents  The Birth of Electromagnetism In 1820, Hans Christian Oersted discovered the magnetic effect of an electric current. His findings saw the birth of electromagnetism. He found that when compasses were placed on different sides of a current-carrying conductor, the needles of the compasses would be deflected in different ways as shown in Fig. 17.5. Following Oersted’s discovery, experiments showed that there is a relationship between the magnetic field due to a current carrying conductor and the current which flows through it. The direction of magnetic field can be determined using Maxwell’s right-hand grip rule as shown in Fig. 17.6. (a) right-hand grip rule for straight wire (b) right-hand grip rule for coil or solenoid Fig. 17.6 Fig. 17.5 I

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