ACJC Electromagnetic Forces Lecture Notes

Anglo-Chinese Junior College Lecture Notes Electromagnetic Forces H2 (9478) JC2 Physics 2026 Page 1 of 30 Electromagnetic Forces Guiding Questions Learning Objectives 1. What is a magnet? Are there magnetic charges? 2. What do field lines represent? Do field lines represent similar things for electric fields and magnetic fields? (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  = I , 0 2 NB r = I and 0Bn = I 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 (d) show an understanding that the magnetic field due to a solenoid may be influenced by the presence of a ferrous core 3. Why is the word “flux” used when talking about a magnetic field? (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 sinFB = Il , 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 magnetic 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 4. Do magnetic fields have effects on electric charges? (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 = (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.

Anglo-Chinese Junior College Lecture Notes Electromagnetic Forces H2 (9478) JC2 Physics 2026 Page 2 of 30 1 Magnetic Field The repulsion or attraction between two bar magnets is familiar to us. Magnets and the magnetic field play a very big role in our everyday lives, f rom simple motors to sophisticated electrical components in our phones. It is useful to describe forces in terms of fields and field lines because the description of fields helps us to intuitively understand forces. The magnetic force is no different. A magnetic field is a region of space where a magnetic force is experienced by • a magnetic material • a current-carrying conductor (not placed parallel to the magnetic field lines) • a moving charge (not moving parallel to the magnetic field lines) Magnetic field lines have similar properties to those of electric field lines. These properties are: • Magnetic field lines are drawn from the north seeking pole to the south -seeking pole. The y represent the direction in which a north seeking pole at that point would move. In other words, the direction that a compass would point towards if it was placed at that point. • The strength of the field is represented by the density of the field lines, i.e., the closer the field lines are to each other, the higher the field strength in that region. • The field lines never cross each other. • The lines always form a closed loop, and will continue inside a magnetic. What is a magnet? Are there magnetic charges? What do field lines represent?

Anglo-Chinese Junior College Lecture Notes Electromagnetic Forces H2 (9478) JC2 Physics 2026 Page 3 of 30 2 Magnetic Flux Pattern Due to Current Carrying Conductors 2.1 Long Straight Wire The magnetic field pattern due to a current in a long straight wire is a circular pattern centred on the wire. Measurements show that the field is strong close to the wire and becomes weaker with distance away from it. Nature of Science Moment There is a real possibility of confusion when talking about magnetic poles. This partly arises from the origin of our observations of magnetism. When we write “magnetic north pole” what we really mean is the magnetic pole that seeks the geographic north pole”. We often talk loosely about a magnetic north pole pointing to the (geographical) north pole. Misunderstandings can occur because we also know that like poles repel and unlike poles attract. So we end up with the situation that a magnetic north pole is attr acted to the “geographic north pole”, which seems wrong in the context of two poles repelling. More accurately, the north pole of the earth’s magnetic field points to the geographic south and vice versa (see Fig. 1). Adapted from Homer, D. & Bowen-Jones, M., 2014 Ed. Physics IB Course Companion Discovery of magnetic fields around current carrying wire. Fig. 1

Anglo-Chinese Junior College Lecture Notes Electromagnetic Forces H2 (9478) JC2 Physics 2026 Page 4 of 30 Fig. 2.1(a) With no current in the wire, all compass needles point in the direction towards the geographic north pole (magnetic south pole) of the earth. This shows only the earth’s magnetic field is present. Fig. 2.1(b) When current I flows, each compass needle deflects in a direction tangential to a circle. The net magnetic field in the region is circular around the wire. (Earth’s magnetic field is negligible.) Fig. 2.1(c) The direction of the magnetic field could be deduced using the right- hand grip rule. Imagine gripping the wire in your right hand, the thumb points in the current direction and the fingers curl in the direction of the field. Magnetic field lines always form closed loops. (Source: Physics for Scientists and Engineers by Serway) A current flowing in a n infinitely long , straight wire pro duces a magnetic field represented by concentric circular field lines as shown. Fig. 2.2(a) Fig. 2.2(b) current I flowing out-of-page current I flowing into-page N

Anglo-Chinese Junior College Lecture Notes Electromagnetic Forces H2 (9478) JC2 Physics 2026 Page 5 of 30 Points to note: • The field lines are closer together nearer the wire, indicating that the field is stronger nearer the wire. • Direction of B at any point is tangent to the flux line. • Direction of B is always perpendicular to the radial line from the current. • Using the right -hand grip rule, for current flowing out of the page, direction of B is anti- clockwise. Fig. 2.3 In 3-dimension, the magnetic field is represented by a set of concentric cylindrical surfaces, where the perpendicular separation between each surface increases away from the wire, indicating that the field is stronger nearer the wire. The magnitude for the magnetic flux density at a perpendicular distance d of infinite length carrying a current I is given by 2 oB d  = I where 714 10 T m Ao −−= , is the permeability of free space. 2.2 Flat Circular Coil Fig. 2.4 shows the flux pattern around a flat circular coil carrying a current I. The pattern is in a horizontal plane , perpendicular to the coil and passing through its centre. The direction of the magnetic field B due to a current carrying conductor could be deduced using the right-hand grip rule. I B

Anglo-Chinese Junior College Lecture Notes Electromagnetic Forces H2 (9478) JC2 Physics 2026 Page 6 of 30 (Source: Physics for Scientists and Engineers by Serway) (Source: Advanced Physics by Tom Duncan) Fig. 2.4 (a) Fig. 2.4 (b) Fig. 2.4 (c) – Top view of the coil Fig. 2.4 (d) – Front view of the coil The left side of the coil acts like a north pole and the right acts like a south pole. The magnitude for the magnetic flux density at the