The polarity of induced emf is given by

Faraday's Law Faraday's Law Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated. The change could be produced by changing the magnetic field strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic field, rotating the coil relative to the magnet, etc. Faraday's law is a fundamental relationship which comes from R Nave Lenz's Law When an emf is generated by a change in magnetic flux accordingto R Nave Magnet and Coil When a R Nave

As we have seen, any change in magnetic flux induces an emf opposing that change—a process known as induction. Motion is one of the major causes of induction. For example, a magnet moved toward a coil induces an emf, and a coil moved toward a magnet produces a similar emf. In this section, we concentrate on motion in a magnetic field that is stationary relative to the Earth, producing what is loosely called motional emf. One situation where motional emf occurs is known as the Hall effect and has already been examined. Charges moving in a magnetic field experience the magnetic force F = qvB sin θ F = qvB sin θ size 12 is perpendicular to this area, and the area is increasing as the rod moves. Thus the magnetic flux enclosed by the rails, rod, and resistor is increasing. When flux changes, an emf is induced according to Faraday’s law of induction. Figure 23.11 (a) A motional emf = Bℓv emf = Bℓv size 12 is into the page, perpendicular to the moving rod and rails and, hence, to the area enclosed by them. (b) Lenz’s law gives the directions of the induced field and current, and the polarity of the induced emf. Since the flux is increasing, the induced field is in the opposite direction, or out of the page. RHR-2 gives the current direction shown, and the polarity of the rod will drive such a current. RHR-1 also indicates the same polarity for the rod. (Note that the script E symbol used in the equivalent circuit at the bottom of part (b) represents emf.) To find the magnitude o...

In this tutorial we will see that the inductor is an electrical component used to introduce inductance into a circuit which opposes the change of current flow, both magnitude and direction, and that even a straight piece of conductive wire can have some amount of inductance in it. In our tutorials about Electromagnetism we saw that when an electrical current flows through a wire conductor, a magnetic flux is developed around that conductor. This affect produces a relationship between the direction of the magnetic flux, which is circulating around the conductor, and the direction of the current flowing through the same conductor. This results in a relationship between current and magnetic flux direction called, “Fleming’s Right Hand Rule”. But there is also another important property relating to a wound coil that also exists, which is that a secondary voltage is induced into the same coil by the movement of the magnetic flux as it opposes or resists any changes in the electrical current flowing it. A Typical Inductor In its most basic form, an Inductor is nothing more than a coil of wire wound around a central core. For most coils the current, ( i) flowing through the coil produces a magnetic flux, ( NΦ) around it that is proportional to this flow of electrical current. An Inductor, also called a choke, is another passive type electrical component consisting of a coil of wire designed to take advantage of this relationship by inducing a magnetic field in itself or within it...

Faraday’s and Lenz’s Law Faraday’s experiments showed that the emf induced by a change in magnetic flux depends on only a few factors. First, emf is directly proportional to the change in flux Δ Φ Δ Φ size 12. The equation for the emf induced by a change in magnetic flux is 23.2 This relationship is known as Faraday’s law of induction. The units for emf are volts, as is usual. The minus sign in Faraday’s law of induction is very important. The minus means that the emf creates a current I and magnetic field B that oppose the change in flux Δ Φ Δ Φ size 12—this is known as Lenz’s law. The direction (given by the minus sign) of the emf is so important that it is called Lenz’s law after the Russian Heinrich Lenz (1804–1865), who, like Faraday and Henry, independently investigated aspects of induction. Faraday was aware of the direction, but Lenz stated it so clearly that he is credited for its discovery. (See Figure 23.7 (a) When this bar magnet is thrust into the coil, the strength of the magnetic field increases in the coil. The current induced in the coil creates another field, in the opposite direction of the bar magnet’s to oppose the increase. This is one aspect of Lenz’s law—induction opposes any change in flux. (b) and (c) are two other situations. Verify for yourself that the direction of the induced B coil B coil size 12 shown indeed opposes the change in flux and that the current direction shown is consistent with RHR-2. To use Lenz’s law to determine the directions...

Learning Objective By the end of this section, you will be able to: • Calculate emf, force, magnetic field, and work due to the motion of an object in a magnetic field. As we have seen, any change in magnetic flux induces an emf opposing that change—a process known as induction. Motion is one of the major causes of induction. For example, a magnet moved toward a coil induces an emf, and a coil moved toward a magnet produces a similar emf. In this section, we concentrate on motion in a magnetic field that is stationary relative to the Earth, producing what is loosely called motional emf. One situation where motional emf occurs is known as the Hall effect and has already been examined. Charges moving in a magnetic field experience the magnetic force F = qvB sin θ, which moves opposite charges in opposite directions and produces an em f = Bℓv. We saw that the Hall effect has applications, including measurements of B and v. We will now see that the Hall effect is one aspect of the broader phenomenon of induction, and we will find that motional emf can be used as a power source. Consider the situation shown in Figure 1. A rod is moved at a speed v along a pair of conducting rails separated by a distance ℓ in a uniform magnetic field B. The rails are stationary relative to B and are connected to a stationary resistor R. The resistor could be anything from a light bulb to a voltmeter. Consider the area enclosed by the moving rod, rails, and resistor. B is perpendicular to this ar...

Faraday’s and Lenz’s Law Faraday’s experiments showed that the emf induced by a change in magnetic flux depends on only a few factors. First, emf is directly proportional to the change in flux \(\Delta \Phi\). Second, emf is greatest when the change in time \(\Delta t\) is smallest—that is, emf is inversely proportional to \(\Delta t\). Finally, if a coil has \(N\) turns, an emf will be produced that is \(N\) times greater than for a single coil, so that emf is directly proportional to \(N\). The equation for the emf induced by a change in magnetic flux is \[emf = -N \frac\) shown indeed opposes the change in flux and that the current direction shown is consistent with RHR-2. PROBLEM-SOLVING STRATEGY FOR LENZ'S LAW: To use Lenz’s law to determine the directions of the induced magnetic fields, currents, and emfs: • Make a sketch of the situation for use in visualizing and recording directions. • Determine the direction of the magnetic field B. • Determine whether the flux is increasing or decreasing. • Now determine the direction of the induced magnetic field B. It opposes the change in flux by adding or subtracting from the original field. • Use RHR-2 to determine the direction of the induced current I that is responsible for the induced magnetic field B. • The direction (or polarity) of the induced emf will now drive a current in this direction and can be represented as current emerging from the positive terminal of the emf and returning to its negative terminal. For prac...

Two long straight wires of telephone circuit inside a house are coplanar with each other and run parallel to a third long straight conductor that carries a current i = i 0 ​ sin ω t. The wires are at a distance of d 1 ​ and d 2 ​ from the conductor. The conductor induced a noise in the telephone circuit. The rms voltage per unit length of this induced emf is given as α × 1 0 − 5 V. Fill the value of α. (Take d 2 ​ = 2 d 1 ​ , i 0 ​ = l n 2 2 2 ​ ​ A ω = 50 rad/s)