When an ean.J is induced due to a variation in the magnetic flux, the direction of the induced current is such that its electromagnetic effects oppose the cause that is producing it. y ‘To understand Lenz's law consider the following experiment which includes three steps shown in three figures. In this experiment, we have a bar magnet and a coil connected in series with a galvanometer (A). Figure (13-a) ‘The north pole of the bar magnet is approaching the coil. Heinrich Lenz Observation: cone) ‘The current flows in the — coil from left to right. GEES Macnet approaches the coil Interpretation: Interpretation (1) Aico ae GHEE secncsatrs law, the right face of the (a) coil acts as a north-face ‘o repel the approaching orth pole of the magnet. Cope Then the direction of the Magnet moves induced magnetic field away from © (Ay the coil Fig. 13 coil by the induced current is horizontally to the right. Then according to the right hand rule, the induced current flows in the coil from left to right. Interpretation (2): According to Lenz’s law, the direction of the induced magnetic field Bj,q , created by the induced current inside the coil, is horizontally to the right to oppose the inerease of the magnitude of the magnetic field created by the bar magnet at each point inside the coil. Using the right hand rule, the induced current, flows in the coil from left to right, Figure (13-b) Observation: No current is induced in the coil Interpretation: The coil and the bar magnet are at rest relative to each other, then there is no variation in the magnetic flux crossing the coil, so no current is flowing in the circuit. Figure (13-0) The north pole of the bar magnet is displaced away from the coil. Observation: ‘The current flows in the coil from right to left. Interpretatior According to Lenz’s law, the right € of the coil acts as a south-face to attract the outgoing north pole of the magnet. The direction of the induced magnetic field Bq created by the induced current inside the coil is horizontally to the right. According to the right hand rule, the induced eurrent flows in the coil from right to leftApplication 2 icy Consider figure (14). The cursor (C) of a rheostat Rh is displaced in the direction of the green arrow on the figure. 1. Indicate the inducing source and the induced circuit. 2. Explain the existence of the induced current in the lamp L during the displacement of the cursor. 3. Determine the direction of the induced current in coil (D). Solution 1. Inducing source: Coil (A). Induced circuit: Coil (D). 2. During the motion of the cursor of the rheostat, the current flowing in (A) changes, and then the magnetic field B created by (A) at all points of coil (D) changes too. Then (D) is crossed by a variable magnetic flux, so it is the seat of induced electromotive force. A current flows in coil (D) since the circuit is closed. 3. The current flowing in the circuit of coil (A) increases due to the motion of (C), and then the magnitude of the magnetic field B at all points inside coil (D) increases. According to Lenz’s law, the direction of the induced magnetic field Biqg inside (D) is horizontally to the left, to oppose the increase of the magnetic field created by coil (A). According to the right hand rule, the induced current ijqy flows in (D) from right to left. Application 3 i 1. In figure (15), the magnet is rotated by 90” in the anti-clockwise sense beside a conducting loop. Determine the direction of the induced current flowing in the loop during the motion of the magnet. 2. Figure (16) is a diagram of Laplace’s rails. The conducting rod MN forms a closed circuit with an ammeter (A), while placed between the poles of a U-shaped magnet. The rod is given an initial velocity which is directed horizontally to the right. Determine the direction of the induced current in MN during its motion. ‘Solution 7. While rotating the magnet, its south pole approaches the loop. The right face of the loop acts then as a south face to repel the approaching south pole. The direction of the induced magnetic field Bing created inside the loop due Fig. 15 Fig. 16 to the induced current is directed horizontally to the left. According to the right hand rule, the induced current flows in the oop in the clockwise sense (viewed from the right side). 2, During the motion of the rod, the area swept by it increases. According to Lenz’s law, the electromagnetic force created due to the induced current has a direction opposite to that of the motion of the rod, According to the right hand rule, the induced current flows in the circuit in the clockwise sense (i passes in the rod MN from M to N). va Sense rotation Direction of motion of rod —> aA ‘coil (Solenoid); 15) as ‘copper: 5 aor - + Abar magnet; TOUS) MES + A galvanometer, Connecting wires > Procedure and observation > + Connect the galvanometer across the S terminals of the coil ri Fig(17-b) * Move the magnet slowly towards the Fig (17-a) ’ ig coil, you observe that the needle is deviated slightly to the right (Figure 17-a). ; ‘© Move the magnet quickly towards the coil, you observe that the deviation of the needle increases (Figure 17-b). > ‘When the magnet is moved faster, the change in the magnetic flux increases, and the needle shows a larger induced curent due to a greater e.m.. Then, the larger the change in the magnetic flux is, the ater the induced electromotive force becomes. Faraday’s law: The induced electromotive force “'e"” in a circuit at any instant is equal to the opposite of the derivative of the magnetic flux crossing the circuit, with respect to time. [EERE] reset i seemareve vane eis an algebraic quantity. Si 1 To understand the relation between the signs of e and i, we consider a closed ‘conducting loop oriented positively in the clockwise sense. Michael Faraday (1791 - 1867) » In figure (18-a): The magnet is moving. towards the loop. According to Lenz’s law, the induced magnetic field at the center of the loop is directed horizontally to the left. According to the right hand rule, ‘the induced current flows in the circuit in Fig (18-a) Fig (18-b) the negative sense (i<0) ‘While the magnet is moving towards the loop, the magnitude (B) of its magnetic field increases at all points inside the loop, so the magnetic flux «p crossing the loop increases, then: $85 =-- ie < me O , bute = te 0 In figure (18-b): The magnet is moving away from the loop. According to Len2’s law, the induced magnetic field at the center of the loop is directed horizontally to the right. According to the right hand rule, the induced current flows in the loop in the positive sense (i > 0). ‘While the magnet is moving away from the lop, (B) decreases at al points inside the loop, so the magnetic flux decreases, then: 2 < 0, bute =- 5% > e>0 Conclusion: ‘Remark In the phenomenon of electromagnetic induction, when the coil acts as a generator: When the coil aD Then: acts asa receiver: ‘4 Ife>0, i flows in the induced circuit in the chosen positive sense; 4 Ife<0, i flows in the induced circuit opposite to the chosen positive sense. (Studied later)6. The Equivalent Generator Ifa coil, a circuit, or any conductor is crossed by a variable magnetic flux and acts as a generator, the characteristics of this generator are: * Blectromotive force e =— $2 ; * Internal resistance r which is the resistance of the wire forming the coil The conductor is then equivalent to a series combination of an ideal generator of electromotive force e and a resistor of resistance r (Figures 19-2 and 19-b). OD + Fig (19a) Fig (19-b) General ex n of the voltage across a generator Generally, if a coil (or a conductor) in an induced circuit is oriented positively from A to B then: The potential difference between the terminals A and B is given by: [us=tise] crews 192and 19), licatio Jn figure (20), a coil of 100 identical square loops, each of side a= 10 cm, is connected in series with a resistor of resistance R = 45 (2. The internal resistance of the coil is r = 5 , and it is crossed by a uniform magnetic field whose magnitude B varies with time according to the graph of figure (21). 1. Consider the time interval [0 ; 8 s]: a. Determine the algebraic value of the induced electromotive force e; in the coil. b. Deduce the direction of the induced current iin the coil. Se BH ¢. Determine the direction of the © 3 induced current iyagain by using oe Lenz's law. B 08 4, Determine the algebraic value of ar the current i; flowing in the coil. ‘e. Calculate the voltage Uses um oN | 04 f. Draw the circuit of the equivalent generator of this coil. pa ©) 2. Determine the value of the 0. induced current during the time Fig. 20 62 10 12 interval [8 s ; 12}. 3. During the interval [12 s ; 16 s], the expression of the ‘magnitude of the magnetic field is B= 04t-46 (SJ) ‘a, Determine the algebraic value of the induced electromotive force e; in the coil. Deduce the algebraic value of the induced current i; flowing in the coil. b. Calculate the voltage tym. €. The positive sense is reversed, Determine the voltage usqy again. Deduce whether une depends ‘on the choice of the positive sense. 4, Draw, during the interval [0; 16 s}, the variation of uyq as a function of time.