Electric Field

Electromagnetic inductionFaradays Law: The emf induced in a circuit by a changing magnetic field is equal to the negative time rate of change of the magnetic flux m through any open surface bounded by that surface. The circuit of interest consists of a number N of tightly wound turns. In equation form, = -N /t. The direction of the induced emf is such as to always oppose the change in magnetic flux that causes the emf (Lenzs law).

Concepts And Principles

Induced currentJoseph Henry worked in the United States and Michael Faraday worked in England to discern the details of current generated in wire and permanent magnets in motionrelative to each other.

Knowing the magnetic fluxRegardless of what moves, knowing the magnetic flux around a conducting entity will allow determination of current induced.See Figure 29.3 at right and Figure 29.4 below.

Emf and the current induced in a loop Follow Example 29.1. Figure 29.5 illustrates the example.

Example 29.1 Emf and current induced in a loop The magnetic field between the poles of the electromagnet in Fig. 29.4 is uniform at any time, but its magnitude is increasing at the rate of 0.020 T/s. The area of the conducting loop in the field is 120 cm2, and the total circuit resistance, including the meter and the resistor, is 5.0 . A) Find the induced emf and the induced current in the circuit. B) If the loop is replaced by one made of an insulator, what effect does this have on the induced emf and induced current?

Soln:The vector area of the loop is perpendicular to the plane of the loop (we choose it to be vertically upward). Then the vectors A and B are parallel. Since B is uniform, the magnetic flux through the loop is: = BA = BA cos 0o = BA and the rate of change of magnetic flux is: /t = (0.020 T/s)(0.012 m2) = 2.4 x 10-4 V = 0.24 mVThe corresponding induced current is: I = /R = 2.4 x 10-4V/5.0 = 4.8 x 10-5 A = 0.048 mA

B) By changing to a loop made of insulator, weve made the resistance of the loop very high. Faradays law does not involve the resistance of the circuit in any way, so the induced emf does NOT change. But the current will be smaller as given by the equation I = /R.

Check Your UnderstandingA coil is placed in a magnetic field, and the normal to the plane of the coil remains parallel to the field. Which one of the ff. options causes the average emf induced in the coil to be as large as possible?The magnitude of the field is small, and its rate of change is large.The magnitude of the field is large, and its rate of change is small.The magnitude of the field is large, and it does not change.

Lenzs LawThe induced emf resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change. (The direction of any magnetic induction effect is such as to oppose the cause of the effect.)

The emf Produced By a Moving Magnet:The figure shows a permanent magnet approaching a loop of wire. The external circuit attached to the loop consists of the resistance R, which could be the resistance of the filament in a light bulb, for instance. Find the direction of the induced current and the polarity of the induced emf.

S N Magnetic field A B Lines

R

Induced Current

Induced Magnetic field Lines A + - B

Reasoning and Solution:We apply Lenzs law, the essence of which is that the change in magnetic flux must be opposed by the induced B. The through the loop is increasing , since the magnitude of the magnetic field at the loop is increasing as the magnet approaches. To oppose the increase in the flux, the direction of the induced magnetic field must

be opposite to the field of the bar magnet. Since the field of the bar magnet passes through the loop from left to right in part a of the drawing , the induced field must pass through the loop from right to left, as in part b. To create such an induced field , the induced current must be directed counter-clockwise around the loop, when viewed from the side nearest the magnet. The loop behaves as a source of emf, just like a battery. Since conventional current is directed into the external circuit from the positive terminal, point A in Fig. b must be the positive terminal, and point B must be the negative terminal.

MUTUAL INDUCTIONCoil 1 is connected to a voltage source and coil 2 is connected to a lamp. An iron rod is inserted in coil 1. Coil 1 Coil 2

S L Explain each of the ff. observations:

When the switch S is closed:1. change in current from 0 to max; there is induction in coil 1; Right end of coil 1 becomes the N-pole; B is induced in coil 2 with its left end becoming the N-pole hence current in coil2 is directed CCW.Long after the S has been closed, the current is steady; no change in the current or , no induction in coil 2.When the switch S is opened, there is change in current from max. to zero; there is induction in coil 2.Long after the S is closed, coil 1 is moved towards coil 2; there is repulsion between the coils.Long after the S is closed, coil 2 is moved away from coil 1; there is attraction between the coils.Long after the S is closed, the iron rod in coil 1 is removed; there is attraction between the coils.

transformersThe ff. figure shows a simple transformer which has 10 turns in the primary coil and 100 turns in the secondary coil. A) Should the power supply be d.c. or a. c.? B) A p.d. of 15 V exists across the primary coil. What is the p.d. across the secondary coil? C) Is this a step-up or step-down transformer? primary coil secondary coil

power supply output

Solution:Transformers work on a.c.Vs = VpNs/Np = (15 V)(100 turns)/10 turns = 150 VStep-up transformer since the output is higher than the input.

A step-down transformer gives a current of 5 A at 12 V. Assume that there is no power loss. If the primary voltage is 240 V, find:the primary current;the power input; and the power output.

Check your understanding3. 3 kW of power are supplied at the end of power cables of total resistance 10 . Calculate the power loss in the cables if power is transmitted a) at 200 V, b) at 4000 V, c) Is power loss in the cables much less when the power is transmitted at higher voltage OR at lower voltage? d) Is your answer in (c) associated with large current or with small current? e) Based on your answers in (c) and (d) should long-distance power lines be made of thick wires or thin wires? Why?

QUIZ Coil 1 is connected to a voltage source and coil 2 is connected to a galvanometer. Coil 1 Coil 2

A B C D

S

W X Y Z

Modified True or false: Write T if the statement is true and change the underlined word or letter to make the false statement true.

When the switch S in setup 1 is closed:1. coil 1 becomes an electromagnet whose N-pole is labelled A. T 2. magnetic field is induced in the 2nd coil whose N-pole is labelled D. T 3. The induced current in coil 2 causes the galvanometer pointer to deflect to the left. T When the switch is kept closed: 4. the G-pointer does not deflect because no B is induced in coil 2. T

QUIZ NO. 25. the B in coil 1 relative to coil2 is not changing . T When the switch is turned off: 6. the magnetic field in coil 1 reverses in direction. F (does not reverse its direction) 7. End C of coil 2 becomes an N-pole. T 8. The current through the battery is from X to W. T 9. The induced current through the galvanometer is from Z to Y. F (Y to Z)10. A, C