H2 Electromagnetism Lecture Notes (Teachers)

9749 H2 PHYSICS Lecture Notes Nanyang Junior College 1 Chapter 16 ELECTROMAGNETISM Content • Concept of a magnetic field • Magnetic fields due to currents • Force on a current-carrying conductor • Force between current-carrying conductors • Force on a moving charge 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 flux patterns due to currents in a long straight wire, a flat circular coil and a long solenoid (c) use B = µ0I / 2πd, B = µ0NI / 2r and B = µ0nI for the 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 (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 F = B Il sinθ, with direc tions as interpreted by Fleming’s left-hand rule (g) define magnetic flux density and the tesla (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 (j) predict the direction of the force on a charge moving in a magnetic field (k) recall and solve problems using the equation F = BQvsinθ (l) describe and analyse deflections of beams of charged particles by uniform electric and uniform magnetic fields (m) explain how electric and magnetic fields can be used in velocity selection for charged particles

9749 H2 PHYSICS Lecture Notes Nanyang Junior College 2 1 Magnetic Field The idea of a field is a theoretical concept used by scientists to explain how objects interact with one another without physically touching each other. Field lines (flux patterns) are imaginary lines which aid visualization and quantification of the field. A magnetic field is a region of space in which a magnetic material, a current -carrying conductor or a moving charge located in it may experience a force. Magnetic field lines are lines of force as they indicate the direc tion of the force acting on a magnetic North pole. If the lines of force are parallel, the field is uniform. This means that the number of lines passing perpendicularly through unit area at all cross -sections in a magnetic field is the same. If the lines of force are closer together, the field is said to be stronger. Magnetic field lines do not intersect as there can only be one direction for the field at any point. Convention in Representing Field Directions: 1) Field lines around a magnet is represented by lines of force leaving the North pole and entering the South pole 2) Field lines directed in and out of a page are represented by dot and cross diagrams. Gravitational field lines of the Earth Electric field lines of a positive charge Magnetic field lines of a bar magnet Non-uniform magnetic field Uniform magnetic field Cross and dot notation + x x x x x x x x x x x x xx 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 pointing into paper B pointing out of paper

9749 H2 PHYSICS Lecture Notes Nanyang Junior College 3 1.1 Magnetic Flux Pattern of Magnets Since magnetic field lines do not intersect, they interact to produce a resultant line of force at each point. Field lines are not rigid but can be deformed and give way to each other as shown in the diagrams above. 1.2 Magnetic Flux Pattern due to a Current-carrying Conductor When there is a current in a conductor, a magnetic field will be set up around it. The magnetic flux pattern consists of concentric circles, radiating outwards from the conductor. Right Hand Grip Rule is useful in determining the direction of m agnetic field lines. For a current - carrying conductor, the thumb points along the direction of the current while the fingers point in the direction of the magnetic field around the conductor. Example 1 Draw the field lines around the wire from the (i) 3-D view and (ii) side view. Resultant lines of force between two North poles Resultant lines of force between North and South poles Resultant lines of force of a bar magnet Magnetic flux pattern of a piece of wire (ii) (i) I I Current Field Right Hand Grip Rule

9749 H2 PHYSICS Lecture Notes Nanyang Junior College 4 The magnetic flux density B at a perpendicular distance d due to current I in a long straight wire placed in vacuum of permeability µ0 is given by the expression IoB d µ π= 2 1.3 Magnetic Flux Pattern due to Two Current-carrying Conductors Two straight current-carrying conductors can be placed near to one another. Since each conductor creates its own magnetic field, the two magnetic fields will overlap each other and form a resultant magnetic field. The resultant magnetic field can be obtained by the vector addition of individual magnetic field lines. Regions with no resultant magnetic field (neutral points) may also result as indicated by an X. Case 1: Current in the same direction Top View 3-D Side View I X d IoB d µ π= 2

9749 H2 PHYSICS Lecture Notes Nanyang Junior College 5 3-D Side View Case 2: Current in the opposite direction 1.4 Magnetic Flux Pattern due to Flat Circular Coil For a flat circular coil, the Right Hand Grip Rule can also be used to deduce the flux pattern. The thumb points along the direction of the current while the fingers point in the direction of the magnetic field around the coil. The magnetic flux density B at the center of a flat circular coil with N turns of radius r due to current I in placed in vacuum of permeability µ 0 is given by the expression Top View I r IoNB r µ= 2

9749 H2 PHYSICS Lecture Notes Nanyang Junior College 6 IoBn µ= 1.5 Magnetic Flux Pattern due to a Long Solenoid A solenoid consists of many flat circular coils stacked together side by side. The resultant magnetic field can be obtained by the vector addition of magnetic field due to individual flat circular coils. The magnetic flux density B inside a long solenoid with n number of turns per unit length along its axis due to current I in placed in vacuum of permeability µ0 is given by the expression The magnetic field is uniform and the magnetic field lines are parallel along the axis of the solenoid Flux pattern of a solenoid in different orientations n I B B/2 P Q

9749 H2 PHYSICS Lecture Notes Nanyang Junior College 7 1.6 Effect of Ferrous Core A ferrous (iron) core has the ability to align its dipoles in the direction of an external magnetic field . By inserting a ferrous core into a solenoid, the f ield lines are concentrated, thus strengthening the field. The f errous core becomes magnetized and results in a much stronger magnetic field in the same direction. 2 Electromagnetism 2.1 Force on a Current-carrying Conductor When a current -carrying conductor is placed in an external magnetic field, a force will be exerted on it if the field is perpendicular to or has