Introducton Faraday's Law o Inducton In ths lab, you wll study Faraday's Law o nducton usng a wand wth col whch swngs through a magnetc eld. You wll also examne converson o mechanc energy nto electrc energy by comparng the energy dsspated n a load resstor to the loss o mechancal energy o the pendulum wand. A rgd pendulum wth col at ts end swngs through a horseshoe magnet. A resstve load s connected across the col and the nduced voltage s recorded usng a Voltage Sensor and the angle s measured wth a Rotary Moton Sensor whch also acts as a pvot or the pendulum. Graphs o the nduced voltage and angle versus tme are plotted. The power dsspated n the resstor s calculated rom the voltage across the load resstor. The energy converted to thermal energy s determned rom the area under the power versus tme graph. Ths energy s compared to the loss o potental energy determned rom the ampltude o the pendulum. Apparatus Inducton wand, varable gap magnet, large stand and rod, voltage sensor, rotary moton sensor, magnetc eld sensor, Verner nterace devce, multmeter, balance, ruler and computer. Theory Part I: Induced em Accordng to Faraday's Law o Inducton, a changng magnetc lux through a col nduces an em gven by d N (1) dt where B da BA or a magnetc eld (B) whch s constant over the area (A) and perpendcular to the area. N s the number o turns o wre n the col. For ths experment, the area o the col s constant and as the col passes nto or out o the magnetc eld, there s an average nduced em gven B by NA. (2) t The drecton o the nduced voltage as the col enters and leaves the magnetc eld s examned and analyzed usng Lenz' Law. Part II: Energy converson Let L s the dstance rom the axs o rotaton to the center o mass. I the center o mass o the pendulum starts rom rest at a heght h, ts potental energy s U mgh mgl(1 cos ) (3) the heght h s measured rom the lowest poston o the center o mass as shown n Fgure 1. I the ntal and nal heghts are h and h respectvely, then the energy lost s Center o mass h θ θ L where U mg( h h ) (4) h L Lcos and h L Lcos 1 Fgure. 1. Oscllatng Wand
Accordng to the conservaton o energy, t wll be equal to the energy lost to rcton, and energy converted to electrcal energy. For a resstve load n the crcut (R), the electrcal energy s then dsspated as thermal energy. Induced em ( n the crcut s IR Ir where r s the resstance o the col tsel, and I s the current n the crcut. Snce R and r n seres the power (P = I ) n crcut s gven by 2 V P I ( R r) ( R r) (5) R where V s the voltage across the external resstor, V = IR. Thermal energy dsspated n the resstor (R) s gven by Procedure 2 E = P t = Area under power (P) versus t graph. Beore settng up the apparatus or ths lab, measure the ollowng and wrte down n a data sheet. a. The resstance o the col o the nducton wand (r) and the resstor attached n the banana plug (R) separately usng a multmeter. b. Plug the banana plug wth resstor to the end o the wand handle. Locate the center o mass o the wand. Measure the dstance rom the pvot pont to the center o mass (L). c. Mass o the wand ncludng the banana plug (m). d. Fnd the number o turns (N) and area o the col (A) rom the speccaton o the nducton wand. Part I: Induced em by movng col In ths part, the nducton wand s swung nto the magnetc eld. The setup or ths part s shown n the Fgure 3. - Assemble the Rotary Moton Sensor wth Rotary moton the stand. Attach the nducton col wand to sensor the Rotary Moton Sensor. - Adjust the heght o the stand so that the col s n the mddle o the varable gap magnet. Voltage sensor Adjust the gap between the magnet poles to about 1 nch. - Connect the voltage sensor termnals to the nducton wand. [Make sure you are NOT measurng voltage across the load resstor the banana plug s nserted!]. Drape the voltage sensor wres over the rods as shown n Fgure 3 so the wres wll not exert any torque on the col as t swngs. Plug the Voltage probe and Rotary Moton Sensor nto the Verner nterace whch should be connected to a computer. 2 R Inducton wand Magnet Magnet eld sensor Col r Fgure. 2. Equvalent crcut dagram Fgure. 3. Expermental set up or part I
- Now, Open Logger Pro n your computer. Set samplngs rate to 1000 samples/sec and collecton tme to 20 sec. [You may clck Experment and then Data Collecton n the menu bar to change the settng]. Beore takng the data, zero the values by clckng at Ø. Now clck Collect wth the col at rest n ts equlbrum poston between the magnets. Then rotate the wand to some angle (For example = 0.4 rad) and let t go. Clck STOP ater a ew swngs. Analyss 1. Hghlght the rst nduced voltage regon and determne the average voltage. Wrte down the average voltage o the rst peak n your data sheet. 2. Identy on the graph where the col s enterng the magnet and where the col s leavng the magnet. Why s the sgn o the em o the second peak opposte to the sgn o the rst peak? 3. Why s the em nearly zero when the col s passng through the center o the magnet? Explan your answers and nclude the graphs o em and angle vs tme (n the same scale) n your lab report. Estmaton o nduced em, - In order to estmate theoretcal value, measure the magnetc eld between the magnet poles usng the magnetc eld sensor (or use the value provded). Calculate maxmum lux change. - From the graph, determne the derence n tme rom the begnnng to the end o the rst peak ( t). - Calculate the value o the average em usng Faraday s equaton and compare wth your result. Part II: Mechancal to Electrcal Energy Converson For ths part o the lab, the apparatus setup s shown n the Fgure 4 below. Frst, you wll measure the change n potental energy n open crcut condton to determne the energy lost due to rcton and then change n potental energy n a closed crcut condton to determne the energy dsspated n the resstors. Fgure. 4. Expermental set up or part II Fgure.5. Resstor Dsconnected 3
(a) Energy lost due to Frcton - Adjust the gap between the magnet poles. Put the magnet poles as close together as possble but the wand should swng through the magnet wthout httng t. - Plug the load resstor wth one o ts plugs out to the sde and one plug n the wand (see Fgure 5). It makes the crcut open wthout changng the center o mass. - Connect the voltage probe termnals across the load resstor (but the crcut s stll open!). - Make sure the Rotary Moton Sensor probe s connected properly nto the Verner nterace whch should be connected to a computer. Measurement and Analyss - Beore collectng the data, make sure the samplngs rate s 1000 samples/sec and collecton tme s 20 sec. I not adjust them as you dd beore n part I. - Beore takng the data, zero the values by clckng at Ø. Now clck Collect wth the col at rest n ts equlbrum poston between the magnets. Then rotate the wand to an ntal angle (For example = 0.4 rad) and let t go. Clck STOP ater t has swung to the other sde. Repeat the step the rst tral dd not go well. - Determne the angle to whch the pendulum rses ater t passes once through the magnet. Potental Energy (U) versus tme graph You can dsplay a graph o the potental energy versus tme rom the data o angle you just measured rom the rotary moton sensor. Follow the nstructons gven below On the computer, clck New Calculated Column under Data menu. Name t Potental Energy U as short name and Joules n unt. Under the expresson, type the rght hand sde expresson o Eq. (3) as n any computer language. You may drectly use the values or m, g, and L or use them as parameters and then substtute the values. For angle, clck Varables (Columns) and choose (angle). Clck Done to complete. Ths wll add a column or you wth calculated potental energy values correspondng to the angles measured by the rotary moton sensor. - Insert a new graph to dsplay U versus t graph. - Determne the energy lost due to rcton rom ths graph and save the graph. You should nclude ths graph n your report. (b) Energy dsspated by the load resstor - Now, reconnect the load resstor (R) wth both plugs n the wand. Ths completes the seres crcut o the load resstor and col. - Repeat the prevous steps. Clck Collect wth the col at rest n ts equlbrum poston between the cols. Then rotate the wand to an ntal angle ( ) and let t go. Make sure your ntal angle ( ) s same as n the prevous swng n the open crcut case. Clck STOP ater t has swung to the other sde. 4
- Measure the angle to whch the pendulum rses ater t passes once through the magnet. Note the ntal and nal angles. Determne the potental energy lost rom the U versus t graph. Ths s the total energy lost. So, how much s the energy dsspated by the resstor? In order to measure the energy dsspated by the resstor, add a New Calculated Column and Insert a new graph o Power (P) versus tme (t). (Smlar to U versus t, you just dd). Ths tme you are usng eq. (5). - In the Power (P) versus tme (t) graph, hghlght both peaks and nd the area (Integral value). Include ths graph n your report. Ths area s the energy dsspated by the resstors. Why do you need to nclude two peaks? Add the energy dsspated by the resstor and the energy lost to rcton. Compare ths to the total energy lost by the pendulum. Questons: 1. What are the possble errors n ths experment? 2. Hghlght the rst nduced voltage regon and determne the average voltage. What s the average voltage o the rst peak? Is t nduced em? 3. Why s the sgn o the second voltage peak opposte to the sgn o the rst peak? 4. Why s the second peak voltage smaller than the rst one? 5. Why s the voltage nearly zero when the col s passng through the center o the magnet? 5