Physics Lab 202P-9 Magnetic Fields & Electric Current NAME: LAB PARTNERS: LAB SECTION: LAB INSTRUCTOR: DATE: EMAIL ADDRESS: Penn State University Created by nitin samarth Physics Lab 202P-9 Page 1 of 22
Physics Lab 202P-9 Software List EMField Microsoft Excel Equipment List (all items marked with * are in the student kit, others are supplied at the time of the lab) 9V battery Switch *Two 1.5 V batteries + a battery holder *Long (~2 ft) insulated wire *Hookup wires with alligator clips *Compass Penn State University Created by nitin samarth Physics Lab 202P-9 Page 2 of 22
Prelab checkbox: Satisfactory Unsatisfactory Physics Pre-lab 202P-9 Magnetic Fields and Electric Current Name: Section: Date: (Read this & answer the questions before coming to lab) Summary of relevant concepts: When an electric charge moves, it creates a magnetic field. Magnetic field is measured in units of "tesla" (T). Magnetic fields can exert a force on MOVING electric charges; for a charge q moving with a velocity v in a magnetic field B, this force F is given by: r r r F = qv B Since an electric current consists of moving charges, a magnetic field can also exert a force on a current; for a straight wire of length L and carrying a (conventional) current I, the force exerted by a magnetic field B is: r r r F = IL B The magnetic field created by a current can be calculated using two fundamental laws: the Biot-Savart Law and Ampere's Law; The Biot-Savart Law provides an expression for the magnetic field db at a distance R from a differential element of wire dl carrying r a current r I: r µ 0 IdL R db = 3 4 π R Note that this is an INVERSE SQUARE law, similar to Coulomb's Law. Ampere's Law is useful in cases of obvious symmetry and relates the integral of the magnetic field B around a closed loop C to the TOTAL current I through the area bounded by the loop: C r r B dl = µ 0 I Penn State University Created by nitin samarth Physics Lab 202P-9 Page 3 of 22
Pre-lab Questions: Set up the experiment shown in the figure above using two 1.5 V batteries in series and the long insulated wire in your experimental kit. You can make contact to the wire by using a knife or blade to remove ~5 mm of insulation at each end. Make sure you don't use the bare Nichrome wires for this experiment. Then, answer the questions that follow. Note: do not keep the circuit fully connected except for short intervals when making observations -- otherwise you'll use up your batteries! Penn State University Created by nitin samarth Physics Lab 202P-9 Page 4 of 22
Q1. For the polarity of the batteries shown above, the (conventional) current in the wire travels from left to right. Make a qualitative sketch that shows the magnetic field lines produced by this current. Briefly justify your prediction using the Biot-Savart Law. Describe a "right hand rule" that gives you a shortcut for determining the direction of the magnetic field lines produced by a straight wire. Penn State University Created by nitin samarth Physics Lab 202P-9 Page 5 of 22
Q2. Use your magnetic compass to qualitatively confirm your expectations in Q1. Describe briefly how you did this. Remember that the compass is always subject to the Earth's magnetic field, and is also affected by other external factors such as the proximity of other magnetic objects. Keep in mind that magnetic fields obey superposition. Finally, a cautionary note: the painted end of your compass needle is supposed to be the "North" pole of the needle; however, your compass needle may be mislabeled! Check to make sure which end of the needle is "North." Penn State University Created by nitin samarth Physics Lab 202P-9 Page 6 of 22
Q3. What do you expect will happen to the magnetic field lines if the current direction is reversed? Justify this using (a) the right hand rule and (b) the Biot Savart Law. Describe the results of an experiment that tests your prediction. Penn State University Created by nitin samarth Physics Lab 202P-9 Page 7 of 22
Q4. Order of magnitude estimate: what is the approximate magnetic field in the experiment you just carried out at a distance of 1 cm from the center of the wire? Specify your approximations and assumptions. Compare this with the magnetic field of the Earth. Penn State University Created by nitin samarth Physics Lab 202P-9 Page 8 of 22
Q5. Rule of thumb: if you triple your distance from a long current carrying wire, what happens to the magnetic field? What approximations did you make? Carry out an experiment to test this "rule of thumb" and briefly describe what you find. Penn State University Created by nitin samarth Physics Lab 202P-9 Page 9 of 22
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Lab Activity: Magnetic Fields and Electric Current Activity 1: Understanding the Biot-Savart Law Q1. Consider the circular coil of wire shown as a top view in the figure below. Show how to use the Biot-Savart Law to figure out the magnitude and direction of the magnetic field at the point A located at the center of the circle. What is the "right hand rule" that you can use as a shortcut to determine the direction of the magnetic field at A? I A R Penn State University Created by nitin samarth Physics Lab 202P-9 Page 11 of 22
Q2. Develop an experiment that allows you to qualitatively verify your prediction in Q1. Use the following equipment: the insulated long wire in your kit (same one that you used in the prelab), two 1.5 V batteries in series and the compass. Describe your experiment and the results. Here are a few hints: (a) The magnetic field created by a single loop of wire may not be large enough to detect with your compass; is it ok to use several loops? (Think superposition!) (b) In your analysis of Q1, does the shape of the loop make any difference to the direction of the magnetic field inside the loop? (i.e. does it really have to be perfectly circular?) (c) Remember that you are asked for the direction of B inside the loop. Does it make any difference whether you are measuring this exactly at the center? (d) Remember that -- as you found in your prelab -- the compass always measures some background magnetic field in addition to the field created by your experiment. You need to take this into account in making sense of the results of your experiment. Penn State University Created by nitin samarth Physics Lab 202P-9 Page 12 of 22
Q3. Show how to use the Biot-Savart Law to determine the DIRECTION of the magnetic field at any location in the plane of the circular loop but OUTSIDE the loop itself. Compare the direction of this magnetic field to that inside the coil. Note: There are different ways to go about this problem. Use your creativity! Here is a hint for one possible approach: use Biot-Savart for a STRAIGHT wire and then "morph" this into the problem of interest. Penn State University Created by nitin samarth Physics Lab 202P-9 Page 13 of 22
Q4. Carry out and describe an experiment that qualitatively verifies your prediction in Q3. Use the same equipment and hints as in Q2. Penn State University Created by nitin samarth Physics Lab 202P-9 Page 14 of 22
Q5. Using the understanding you developed in Q1-Q4, as well as other considerations such as symmetry, sketch a 3D view of the magnetic field lines created by a circular loop of current. Describe how you arrived at this picture. How would your picture change if the direction of the current in the coil were reversed? Penn State University Created by nitin samarth Physics Lab 202P-9 Page 15 of 22
Activity 2: Magnetic Force on a Current Carrying Wire Set up the experiment shown below but do NOT complete circuit except for the brief periods when you are instructed to in the experimental procedure. Note that the insulated wire in your kit will obviously not allow you make the ideal shape shown in the figure. This is not really important: the only thing that matters is that you have a roughly straight horizontal portion of the wire dangling above your magnet. 9V switch Scotch tape Insulated Wire Bar Magnet Penn State University Created by nitin samarth Physics Lab 202P-9 Page 16 of 22
Q6. Use your compass to determine which end of your magnet is "North." Position your magnet with the N pole immediately below a roughly horizontal straight portion of your wire. Note down the direction in which current will flow when the circuit is completed. Switch the current flow on for a few seconds. Describe and explain the reaction of the wire, using a clear sketch to illustrate your explanation. Repeat the experiment with the S pole of the magnet pointing upwards. Describe and explain the reaction of the wire. Penn State University Created by nitin samarth Physics Lab 202P-9 Page 17 of 22
Q7. Repeat the entire experiment in the earlier question after switching the polarity of the voltage source. Describe and explain the reaction of the wire for both orientations of the magnet. Use clear sketches to illustrate your answers. Penn State University Created by nitin samarth Physics Lab 202P-9 Page 18 of 22
Activity 3: Simulating Magnetic Fields from Currents and Ampere's Law In this activity, we use EMFIELD to visualize the magnetic field created by different arrangements of straight wires carrying a current. The program also allows us to examine how Ampere's Law works. Start EMFIELD from the Physics program group under the START menu. From the "Display" menu, select "Show grid" and "Constrain to grid"; From the "Sources" menu, select "2D line currents"; From the array of positive and negative currents at the bottom of the screen, select appropriate currents and position them to represent the arrangement shown in the figure below. Note that a "positive" current is one that comes out of the screen towards you, while a "negative" current is one that goes into the screen away from you. From the "Fields and potential" menu, you can select the following options: Field vectors: When you click at any point on the screen, the program will draw a vector whose length and direction represent the magnetic field vector at that point. Directional arrows: When you click at any point on the screen, the program will draw an arrow that shows only the direction of the magnetic field at that point. Field lines: When you click at any point on the screen, the program will now show you the magnetic field line passing through that point. Ampere's Law: When you click and drag a closed loop, the program calculates the integral in Ampere's Law. Set up the arrangement shown in the figure below in which the 4 current carrying wires are arranged on the corners of a square. Positive currents are directed out of the page, while negative currents go into the page. The points A, B and C are located on a straight line that bisects the top and bottom sides of the square. Point A is at the CENTER of the square. The distance AB is 1/6 the side of the square and the distance AC is 2/3 the side of the square. Use EMFIELD program to answer the questions on the following page. A word of caution: the program makes mistakes in regions where the magnetic field is very small! Use physical intuition and common sense in interpreting your results! C +9 A +9 A B A -5 A -5 A Penn State University Created by nitin samarth Physics Lab 202P-9 Page 19 of 22
Q8. Use the Biot-Savart Law to figure out the direction of the magnetic field at locations A, B and C. Confirm your answer using EMFIELD. Penn State University Created by nitin samarth Physics Lab 202P-9 Page 20 of 22
Q9. Use the Biot-Savart Law to figure out the relative magnitudes of the magnetic field at A, B and C i.e. rank them in order of increasing strength. Confirm your answers using EMFIELD. Penn State University Created by nitin samarth Physics Lab 202P-9 Page 21 of 22
Q10. According to Ampere's Law, what is the value of the integral r r B dl C for the paths A and B traversed as shown below? Explain your answers. Confirm your answers using EMFIELD. A +9 A +9 A -5 A -5 A +9 A +9 A -5 A -5 A B Penn State University Created by nitin samarth Physics Lab 202P-9 Page 22 of 22