# [Get Solution] Magnetic Field

Magnetic Field Due to Current in Wire Lab Virtualhttp://www.thephysicsaviary.com/Physics/Programs/Labs/FieldFromWire/index.htmlBackground:Hans Ørsted accidentally discovered the fact that electric currents create magnetic fields when he was working with an electric circuit and noticed that, when current was flowing in the circuit, the need of a compass on his desk would deflect. Thus began the investigation of the nature of magnetic fields produced by currents.Instructions:Open the web page listed at the top of this lab. Click Begin. When you do, you will see a screen that has a long gray wire with small blue circles moving to the right (representing the flow of charge). There are many concentric circles around the wire, representing the magnetic field produced by the wire. A small black bar sticking out from the top left represents a magnetic field sensor. The + sign at the right side of the black bar is the point on the sensor where it takes data.Experiment 1: Dependence of Horizontal PositionOpen excel or your favorite spreadsheet program (Google sheets, whatever).Click Location of Field Sensor. Doing so opens a tab that has four arrows: up, down, left, and right. Clicking these arrows allows you to move the sensor around.Click Field Strength in the top right of the panel. This gives the strength of the magnetic field in microTesla (?T).Make sure you measure the field strength in Tesla, not microTesla. So if the measured strength is 5.1?T, your measured value should be 0.0000051T.Brief note on magnetic field strength values that fluctuate: in real life, when measuring values with something like a magnetic field strength sensor, the measured value may fluctuate. For our purposes here, look at the digit to the right of the decimal point and round to the average value of that digit. For example, if you see values such as 12.41 ?T, then 12.32 ?T, then 12.53 ?T, round to 12.4 ?T, then convert to Tesla.Move the field sensor all the way to the left and leave its vertical position unchanged.In your spreadsheet, make two columns:Column 1 is Horizontal PositionColumn 2 is Field strengthSet the initial position of the horizontal position to be 0.005m and take the measured field strength at the position.Move the field sensor to the right (you may assume each step is 0.005m) and not the field strength for each position. You should make 17 steps for a total of 18 different horizontal positions. Each of these positions will have a measured field strength.Graph your data of Field strength vs. horizontal position, making sure you create a complete graph (axis labes, axis units, title, etc.). What do you notice about the trend in your graph? What does this imply about the dependence of field strength on horizontal position near a long wire carrying currentExperiment 2: Dependence on radial positionMove the sensor to the farthest right position, then down as close as possible to the wire. You may assume that this position is 0.01m from the wire.Create a second set of two columns on your spreadsheet:Column 1 is Radial DistanceColumn 2 is Field StrengthNote the position and field strength for this initial position in your spreadsheet.Move the sensor one space up away from the wire (you may assume that the step size is 0.005m). Note the field strength. You should be able to measure the strength of 15 total positions, including the initial position.Graph your data of Field strength vs. radial distance, making sure you create a complete graph (axis labes, axis units, title, etc.). What do you notice about the trend in your graph? What does this imply about the dependence of field strength on radial distance near a long wire carrying current?Aside: Linearizing your dataAs you can probably see, the graph of your data from experiment 2 does not fall on a straight line. Inspection of the shape of the graph shows that your data fall on a 1/x dependence. In order to linearize your data, do the following steps:Copy your position data in meters into a new column.Make a second column next to this where each value is the reciprocal of the position in the first column.For example, if your position value is 0.04m, the reciprocal value will be 1/0.04 = 25Once you have completed this second column of reciprocals, copy your original field strength values into a third column to the right of this one.This means that ever field strength value is next to the reciprocal of the original position as opposed to being next to the original positionGraph your field strength versus the reciprocal position data. What shape does this graph have?Add a trendline to your graph. Display the equation of the trend line. The trendline will have a format y=mx +b, where m is the slope of the trendline. Copy this value into your notes.Why did we do all this? Because the equation of for the magnetic field strength due to a current in a wire is given byWhere B is the field strength in Tesla, I is the current in Amperes, and R is the radial distance from the wire in meters. If we lump everything together on the right side other than the radial distance, we getWhich, if plotted on a graph, would yield a straight-line graph if you plot B vs. 1/R and m would be the slope of that line. That meansthatWhich we can use to solve for the current in the wire. Take the value of the slope from your linearized graph above (the value you got from your equation of the trendline) and use the equation above to solve for the current I. Then, go back to the simulation and click on current in the bottom right corner. Calculate the %difference between your value and the value used in the simulation.Experiment 3: Dependence on currentPlace the sensor all the way to the right and 8 steps above the wire (corresponding to a position of 5cm = 0.05m away from the wire.If you cannot already see the value of the current, click on current in the bottom right corner to display the current. Click the down arrow until the current is 0.0A. Your sensor should read a field strength of 0?T.Use the up arrow to increase the current by one step. Record the current and field strength in your spreadsheet.Continue until you have maximized the current. There should be 9 total values above 0.0A. Record the corresponding field strength values in your spreadsheet.Graph the field strength vs. current data. What trend do you see?As you increase the current, the circles around the wire get darker. What does this indicate?