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Measuring Permittivity of Free Space

Course

University Physics Ii (PHYS 2074)

360 Documents

Students shared 360 documents in this course

University

University of Arkansas

Academic year: 2018/2019

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Arais Verde

University of Arkansas

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Measuring Permittivity of Free Space Lab Report Logan Campbell, Blake Fasse, Arais Verde, Anelisse Claros Physics II : Summer 2019 Purpose The main objective for the lab activity Measuring Permittivity of Free Space is to predict the capacitance of an isolated capacitor to an exact measure and to compare calculated theoretical permittivity of free space. Using a few items such as a spherical conductor, a ground, a capacitance meter , and a ruler to enable comparisons from calculated and measured permittivity of free space. There are two general operations for this lab which are to : obtain a isolated conductor, place a positive charge on the conductor, compute the electric field using law to gather how electricity flows within a surface (which is spherical) Esphere 2 , obtain the potential difference to get a 0r Q capacitance C using that information. The other operation for this lab is to exhibit the theoretical result of measuring permittivity of free space and compared permittivity of free space developing a linear relationship linking the capacitance between two parallel plates and the separation between plates. Using spacers, measurements, and the capacitance equation C to analyze and compare the permittivity of free space(s) from the two parallel plates. Theory Capacitance of a Spherical Capacitor There are several calculations and expressions that need to be addressed before continuing with procedures. Permittivity of Free Space, Law, Potential Difference, and Capacitance all have a mathematical equation and few concepts that need to be understood. Permittivity of Free Space can be represented as how much electric flux (or flow of electricity within a surface) an object can allow. Law express as Hb E dA and for a sphere the radius has the same magnitude across the surface. a Q Q EA r Once the electric field of conducting sphere is gathered. Determining the potential difference (voltage) is needed to express the relationship between potential energy, the charge, and the capacitance. Potential Ha Notice that Q is a constant difference is found integrating the electric field along the sphere. b E flux EA within the integral leaving the radius to be integrated. I b Q 1 Q 1 1 dr a r2 a b Capacitance of a conductor is the ratio of charge on the potential difference. Take the limits from a to b where a goes to our radius and the b goes to infinity. Doing this calculation shows that the charge is spread out over the surface of the sphere. Q lim 1 1 a b a b The setup of the station is illustrated above. Furthermore, zero out the capacitance meter before reading the measurements. Once this is done compare the results from the calculated values and the measure values the procedures are done correctly the measurements should be similar to the capacitance calculated. In the case of this experiment: the radius of the sphere was 12 converted to meters to be .127m where we used the equation C R (.127m) 1 14 pF in result from this experiment the two measurements of capacitance is the same. Proving that the equation is generally valid in theoretical prediction and confirmation. In the next set of procedures, two (17 cm x 17 cm) conductive plates are going to be used to find the permittivity of free space using the capacitance, and a few spacers. Setup two planes with the spacers (2 mm thick) on the edges of the corners of the conductive planes. Connect the a positive wire to the meter and to a plane and then connect the opposite plane with a negative wire reverting back to the meter in the negative slot on the meter. Capture the capacitance, first zeroing the meter then setting the meter to 20mA to see what the Farads are. Do this 6 times with increasing the amount of spacers each iteration one. note: do not out the meter each iteration, do it only once. Record the different amounts of Capacitance and collect the data to continue the experiment. Data The Measurements: Parallel Planes Identify the Area of the plane(s): Aplane 1 m Where slope is equal to the theoretical permittivity of free space slope A 3 8 1 1 Measurements of Parallel Planes Spacers 1 2 3 4 5 6 Separation d(cm) 0 0 0 0 1 1 Separation d(m) 2 4 6 8 10 12 ) 473 236 157 118 95 79 1 d Capacitance (F ) 156 82 63 58 49 44 Capacitance vs Inverse Separation Graphical Correlations m 4 1012 Using the Area (A) to compute from the slope : slope solve for : A 2 4 1012 12 C 1 10 3 N m2

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