E-Physics Tutorial Book

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Activity 1.

Directions: Discuss and elaborate based on the readings presented in the Lesson 1.

Magnets and Magnetic Fields 1.1 Magnetism We have observed a magnet attract paper clips, nails and other objects made of iron. Any magnet, whether it is in the shape of a bar or a horseshoe, has two ends or faces, called poles, which is where the magnetic effect is strongest. If a bar magnet is suspended from a fine thread, it is found that one pole of the magnet will always point toward the north. It is not known for sure when this fact was discovered., but it is known that the Chinese were making use of it as an aid to navigation by the eleventh century and perhaps earlier. This is the principle of a compass. A compass needle is simply a bar magnet which is supported at its center of gravity so that it can rotate freely. The pole of a freely suspended magnet that points toward geographic north called the north pole of the magnet. The other pole points toward the south and is called the south pole. Before the relationship of magnetic interactions to moving charges was understood, the interactions of permanent magnets and compass needles were described in terms of magnetic poles. If a bar-shaped permanent magnet, or bar magnet, is free to rotate, one end points north. This end is called a north pole or N pole; the other end is a south pole or S pole. Opposite poles attract each other, and like poles repel each other (Fig.1). An object that contains iron but is not itself magnetized {that is, it shows no tendency to point north or south) is attracted by either pole of a permanent magnet (Fig. 2}. This is the attraction that acts between a magnet and the unmagnetized steel door of a refrigerator. By analog: to electric interactions, we describe the interactions in Figs. 1 and 2 by saying that a bar magnet sets up a magnetic eld in the space around it and a second body responds to that eld. A compass needle tends to align with the magnetic field at the needle's position. (a) Opp-mill; palm. attract. (3) IN , E. (b) IJLC pulxs- lapel. Figure 1. (a) Two bar magnets attract when opposite poles (N and Figure 2. (a) Either pole of a bar magnet S, or S and N) are next to each other. attracts an unmagnetized object that contains b) The bar magnets repel when like iron, such as a nail. (b) A real-life example of poles (N and N, or S and S) are next this effect. to each other. Photo credit: University Physics with Photo credit: University Physics with Modern Modern Physics 13th edition Physics 13th edition Earth's Magnetic Field The earth itself is a magnet. Its north geographic pole is close to a magnetic south pole, which is why the north pole of a compass needle points north. The earth's magnetic axis is not quite parallel to its geographic axis (the axis of rotation), so a compass reading deviates somewhat from geographic north. This deviation, which varies with location, is called magnetic declination or magnetic variation. Also, the magnetic field is not horizontal at most points on the earth's surface; its angle up or down is called magnetic inclination. At the magnetic poles the magnetic field is vertical. Figure 3 is a sketch of the earth's magnetic field. The lines, called magnetic field lines, show the direction that a compass would point at each location. The direction of the field at any point can be defined as the direction of the force that the field would exert on a magnetic north pole. North geographic pole The geomagnetic north pole is actually (earth's rotation axis) a magnetic south (S) pole-it attracts the N pole of a compass. Figure 3. A sketch of the earth's magnetic Compass field. The field, which is -Magnetic field lines show caused by currents in the direction a compass the earth's molten core, would point at a given changes with time; location. geologic evidence The earth's magnetic shows that it reverses field has a shape direction entirely at similar to that pro- irregular intervals of duced by a simple bar magnet (although 104 to 106 years. actually it is caused by electric currents in the core) Photo credit: The earth's magnetic axis is University Physics with offset from its geographic axis. Modern Physics 13th edition The geomagnetic south pole is actually a South geographic pole magnetic north (N) pole. 1.2 Magnetic Field To introduce the concept of magnetic field properly, let's review our formulation of electric interactions in the previous lessons, where we introduced the concept of electric field. We represented electric interactions in two steps: 1. A distribution of electric charge at rest creates an electric field E in the surrounding space. 2 . The electric field exerts a force F = qE on any other charge q that is present in the field.We can describe magnetic interactions in a similar way: 1. A moving charge or a current creates a magnetic field in the surrounding space (in addition to its electric field). 2 . The magnetic field exerts a force F on any other moving charge or current that is present in the field. Like electric field, magnetic field is a vector field-that is, a vector quantity associated with each point in space. We will use the symbol B for magnetic field. At any position the direction of B is defined as the direction in which the north pole of a compass needle tends to point. The arrows in Fig. 3 suggest the direction of the earth's magnetic field; for any magnet, points out of its north pole and into its south pole The Definition of B We determined the electric field E at a point by putting a test particle of charge q at rest at that point and measuring the electric force FF acting on the particle. We then defined E as E FE (Eq. 1) If a magnetic monopole were available, we could define B in a similar way. Because such particles have not been found, we must define B in another way, in terms of the magnetic force FB exerted on a moving electrically charged test particle. Moving Charged Particles. In principle, we do this by firing a charged particle through the point at which B is to be defined, using various directions and speeds for the particle and determining the force FB that acts on the particle at that point. After many such trials we would find that when the particle's velocity v is along a particular axis through the point, force FB is zero. For all other directions of v, the magnitude of FB is always proportional to v sino, where o is the angle between the zero-force axis and the direction of v. Furthermore, the direction of FB is always perpendicular to the direction of v. (These results suggest that a cross product is involved.) The Field. We can then define a magnetic field B to be a vector quantity that is directed along the zero-force axis. We can next measure the magnitude of FB when is directed perpendicular to that axis and then define the magnitude of B in terms of that force magnitude: FB B = lalv' (Eq. 2) where q is the charge of the particle. We can summarize all these results with the following vector equation: FB = qu x B; (Eq. 3)that is, the force FB on the particle is equal to the charge q times the cross product of its velocity v and the field B (all measured in the same reference frame). Using the cross product, we can write the magnitude of FB as FB = IqlvB sin d, (Eq. 4) where o is the angle between the directions of velocity v and magnetic field B. SI Unit for Magnetic Field The SI unit for that follows from Eq. 3 and 4 is the newton per coulomb-meter per second. For convenience, this is called the tesla (T): newton 1 tesla = 17 = 1- meter (coulomb) (second Recalling that a coulomb per second is an ampere, we have newton N 1T =1 (coulomb) (second) A . m An older name for the tesla is the "weber per meter squared" (1 2 = IT) An earlier (non-SI) unit for B, still in common use, is the gauss (G), and 1 tesla = 104 gauss 1G = 10-4T A field given in gauss should always be changed to teslas before using with other SI units. 1.3 Electric Field vs. Magnetic Field Electric Field Magnetic Field O Byjus.com Figure 4. An Electric field and Magnetic field lines Photo credit: Byjus.com An object with a moving charge always has both magnetic and electric fields. They have some similarities and also have two different fields with the same characteristics. Both fields are inter-related called electromagnetic fields, but they are not dependent on each other. The magnetic field is an exerted area around the magnetic force. It is obtained by moving electric charges. The direction of the magnetic field is indicated by lines. While the electric fields are generated around the particles which obtainelectric charge. During this process, positive charges are drawn, while negative charges are repelled. The area around a magnet within which magnetic force is exerted, is called a magnetic field. It is produced by moving electric charges. The presence and strength of a magnetic field is denoted by "magnetic flux lines". The direction of the magnetic field is also indicated by these lines. The closer the lines, the stronger the magnetic field and vice versa. When iron particles are placed over a magnet, the flux lines can be clearly seen. Magnetic fields also generate power in particles which come in contact with it. Electric fields are generated around particles that bear electric charge. Positive charges are drawn towards it, while negative charges are repelled. A moving charge always has both a magnetic and an electric field, and that's precisely the reason why they are associated with each other. They are two different fields with nearly the same characteristics. Therefore, they are inter-related in a field called the electromagnetic field. In this field, the electric field and the magnetic field move at right angles to each other. However, they are not dependent on each other. They may also exist independently. Without the electric field, the magnetic field exists in permanent magnets and electric fields exist in the form of static electricity, in absence of the magnetic field. 1.3a. What are Electric and Magnetic Fields? Magnetic fields are created whenever there is a flow of electric current. This can also be thought of as the flow of water in a garden hose. As the amount of current flowing increases, the level of magnetic field increases. Magnetic fields are measured in milliGauss (mG). An electric field occurs wherever a voltage is present. Electric fields are created around appliances and wires wherever a voltage exists. You can think of electric voltage as the pressure of water in a garden hose - the higher the voltage, the stronger the electric field strength. Electric field strength is measured in volts per meter (V/m). The strength of an electric field decreases rapidly as you move away from the source. Electric fields can also be shielded by many objects, such as trees or the walls of a building. 1.3b. Nature An electric field is essentially a force field that's created around an electrically charged particle. A magnetic field is one that's created around a permanent magnetic substance or a moving electrically charged object. 1.3c. Movement In an electromagnetic field, the directions in which the electric and magnetic field move, are perpendicular to each other 1.3d. Units The units which represent the strengths of the electric and magnetic field are also different. The strength of the magnetic field is represented by either gaussor Tesla. The strength of an electric field is represented by Newton per Coulomb or Volts per Meter. 1.3e. Force The electric field is actually the force per unit charge experienced by a non moving point charge at any given location within the field, whereas the magnetic field is detected by the force it exerts on other magnetic particles and moving electric charges. However, both the concepts are wonderfully correlated and have played important roles in plenty of path breaking innovations. Their relationship can be clearly explained with the help of Maxwell's Equations, a set of partial differential equations which relate the electric and magnetic fields to their sources, current density and charge density. Difference Between Electric Field and Magnetic Field Electric Field Magnetic Field Nature It creates an electric charge Creates an electric charge in surrounding around moving magnets Units Measured as newton per Measured as gauss or tesla coulomb Force Proportional to the electric Proportional to charge and charge speed of electric charge Movement in Perpendicular to the Perpendicular to the electric Electromagnetic field field magnetic field Measuring An electric field is measure The magnetic field is device is measured using an measured using the electrometer magnetometer 1.4 Magnetic Flux Magnetic flux is a measure of the number of magnetic field lines passing through an area (the product of the average magnetic field times the perpendicular area that it penetrates). The symbol we use for flux is the Greek letter capital phi, The equation for magnetic flux is: D = BA cose, where 0 is the angle between the magnetic field B and the area vector A . The area vector has a magnitude equal to the area of a surface, and a direction perpendicular to the plane of the surface. The SI unit for magnetic flux is the weber (Wb). 1 Wb = 1 T m2. Faraday's law states that an induced current is produced whenever the flux changes. The flux depends on the magnetic field B, area A, and the angle 0. A change in any of these three factors constitutes a change in flux.Fig. A. To maximize the magnetic flux through a flat (a) (b) area, orient the area so the plane of the area is perpendicular to the direction of the magnetic field. (a) shows a perspective view, while (b) shows the view looking along the field lines. In this case, the area vector is in the same direction as the field lines. (Full faced area perpendicular to the magnetic field gives a maximum magnetic flux) Fig. B. There is no flux when the plane of the area (a) (b) is parallel to the field. (a) shows a perspective view, while (b) shows the view looking along the field lines. In this case, the area vector is perpendicular to the field lines. (An area must be perpendicular to the magnetic field) Fig. C. Tilting the loop from the orientation in Figure (a) (b) A reduces the flux. (a) shows a perspective view, while (b) shows the view along the field lines. (Lesser exposure of surface area means lesser flux) Example The figure below is a perspective view of a flat surface with area 3.0 cm2 in a uniform magnetic field B. The magnetic flux through this surface is +0.90 mWb. Find the magnitude of the magnetic field and the direction of the area vector A. (a) Perspective view (b) Our sketch of the problem (edge-on view) 120 Figure D. (a) A flat area A in a uniform magnetic field B (b) The area vector A makes a 60 angle with B. (If we had chosen A to point in the opposite direction, 0 would have been 120 and the magnetic flux PB would have been negative.) Solution Identify and Set Up: Our target variables are the field magnitude B and the direction of the area vector. Because Bis uniform, B and 0 are the same at all points on the surface. Hence, we can use PB = BA cose Execute: The area A is 3.0x10-4m; the direction of A is perpendicular to the surface, so 0 could be either 60 or 120. But PB, B, and A are all positive, so cose must also be positive. This rules out 120, so 0 = 60, see figure above. Hence, we findActivity 1. Directions: Discuss and elaborate based on the readings presented in the Lesson 1 (In paragraph form). 1. Similarities between electric and magnetic fields? (In paragraph form) 2. Differences between electric and magnetic field? (In paragraph form)