RE_Computational - Lab Report Example

Computational Lab #4 Worksheet I. Faraday Magnet Faraday’s law of induction. Include the equation for this in both differential and integral form. The emf that is induced in a circuit is proportional to the time rate of change of the magnetic flux linking that circuit.2. When you get the simulation working save a screenshot. You should notice that there are three types of vectors (arrows) in the simulation. Label these vectors. NOTE: It’s sufficient to explain what these vectors are and where they are on the simulation.

The vectors represented by the arrows in the simulation are:a) Magnetic field: These show the extent of the magnetic field. It is perpendicular to the electric fieldb) Electric field: These arrows show the extent of the electric current within the electric field. It is perpendicular to the magnetic fieldc) Direction of the electric field. It cuts through the electric and magnetic field.3. Change the dipole moment (mu) of the magnet. Describe what effect this has on the simulation. Save a screenshot.

Changing the dipole moment of the magnet changes the extent of the magnetic field. A lower value of the dipole moment will reduce the magnetic field while a high value will result into a larger magnetic field on the simulation. II. Positron in an Electromagnetic Wave4. What is the angle between the E-fields and B-fields in electromagnetic waves? Are EM waves transverse or longitudinal? The angle between the E-fields and B-fields in electromagnetic waves is 900. EM waves are transverse. 5. Save a screenshot of the simulation once you get it working.

What physical quantity is used to trace the particle’s trajectory? The velocity of the particle is used to trace the trajectory of the particle. 6. Do the simulation for an electron. Save a screenshot. How does this differ from that of a positron? The trajectory of the electron simulation is half that of the positron. Introduction (4-6 sentences):In this lab, the simulation involved the behavior of dipoles in a magnetic field. In this exercise, we were able to determine the electromagnetic field which is given by: The magnetic flux is also determined given by the formula;The third simulation was used to determine the self inductance in the magnetic field given by;The three physical quantities were placed at the end of each function in order to allow the one to understand what he/she is dealing with.

Data sheets:Figure 1: Simulation of the vectorsFigure 2: Trajectory for the Simulation of the positronFigure 3: Trajectory for the Simulation of the electronData sheetsscene.height0600scene.xscene.y00scene.backgroundcolor.black0initialize some parameterslambda and omegalamba.600omega2"pi.c/laMbsw.lamb/40.* set up positions for visualization of EM fieldxxarange(-2*lamb,2.0001*lamb,lamb/20.)# set up visualization arrows for electromagnetic field (light)xnatvector(1,0,0)Evec(1BVeC.(1xxx: E fieldea.arrow(pos.(x,0,0), axis.

(0,1amb/10.,0), color.(1.,.6,0),shaftwidth.sw)* B fieldbaarrow(pos.(x,0,0), axis -(0,0,0), color.(0,1,1),shaftwidth.sw)ea.BbeEvec.append(ea)initializet.0.dtlamb/c/900.E01.0e4scalingescalelamb/EOfacalelamb/(2.1e-15)* charge positive for positron, negative for electronpq. +1.6e-19* set up a positronpositron.ephere(pos.(-2.1amb,0,0),radius-lamb/25., color.color.red,m.9e-31, p.vector(0,0,0),crpg)Opwvector(0,0,0.1e-21)set up an electron visualizationpositron.g < 0:positron.color.color.blueset up arrows for particlepositron.visible.1positron.

traiicurve(color.positron.color, radius -4.5)positron.Farrow(pos.positron.pos, axis -(0,0,0), colormcolor.green,shaftwidth.sw)* initialize velocityVvector(0,0,0)scene.autoscale . 0flag . 0t-0ifdynamic loop- runforever1:rate(200)tt+dtS calculate E field axis dimensionsEvec:ea.axis(0,(E0.escale).cos(omega.t - 2.pi.ea.x/lamb),0)ea.B.axiscross(xhat, ea.axis)..7Icalculate E and B vector locationnnEO.cos(omegeot - 2.p1.pos1tron.x/lamb)vector(0,nn,0)Bvector(0,0,nn/c)Uforce fromEfieldFe.positronovEforce from B fieldFbpositron.g.cross(v,B)calculate force axis dimensionpositron.F.axis(Fe+Fb).

fscaleIcalculate force positionHOthe arrow tracks the particlepositron.F.pospositron.poscalcuate momentum (MOMENTUM PRINCIPLE)positron.p • positron.pflFe+Fbp.dt*velocity(positron.p/positron.m)particle positionpositron.pospositron.pos + v.dtIvisualize previous motion of particlepositron.trail.append(pos.positron.pos)data sheet 2scene.height0600scene.xscene.y00scene.backgroundcolor.black0initialize some parameterslambda and omegalamba.600omega2"pi.c/laMbsw.lamb/40.* set up positions for visualization of EM fieldxxarange(-2*lamb,2.

0001*lamb,lamb/20.)# set up visualization arrows for electromagnetic field (light)xnatvector(1,0,0)Evec(1BVeC.(1xxx: E fieldea.arrow(pos.(x,0,0), axis.(0,1amb/10.,0), color.(1.,.6,0),shaftwidth.sw)* B fieldbaarrow(pos.(x,0,0), axis -(0,0,0), color.(0,1,1),shaftwidth.sw)ea.BbeEvec.append(ea)initializet.0.dtlamb/c/900.E01.0e4scalingescalelamb/EOfacalelamb/(2.1e-15)* charge positive for positron, negative for electronpq. +1.6e-19* set up a positronpositron.ephere(pos.(-2.1amb,0,0),radius-lamb/25., color.color.red,m.9e-31, p.

vector(0,0,0),crpg)Opwvector(0,0,0.1e-21)set up an electron visualizationpositron.g < 0:positron.color.color.blueset up arrows for particlepositron.visible.1positron.traiicurve(color.positron.color, radius -4.5)positron.Farrow(pos.positron.pos, axis -(0,0,0), colormcolor.green,shaftwidth.sw)* initialize velocityVvector(0,0,0)scene.autoscale . 0flag . 0t-0ifdynamic loop- runforever1:rate(200)tt+dtS calculateEfieldaxisdimensions-eaEvec:ea.axis(0,(E0.escale).cos(omega.t - 2.pi.ea.x/lamb),0)ea.B.axiscross(xhat, ea.axis)..

7Icalculate E and B vector locationnnEO.cos(omegeot - 2.p1.pos1tron.x/lamb)vector(0,nn,0)Bvector(0,0,nn/c)Uforce fromEfieldFe.positronovEforce from B fieldFbpositron.g.cross(v,B)calculate force axis dimensionpositron.F.axis(Fe+Fb).fscaleIcalculate force positionHOthe arrow tracks the particlepositron.F.pospositron.poscalcuate momentum (MOMENTUM PRINCIPLE)positron.p positron.pflFe+Fbp.dt*velocity(positron.p/positron.m)particle positionpositron.pospositron.pos + v.dtvisualize previous motion of particlepositron.trail.append(pos.positron.pos)Conclusion (4-6 sentences):The simulation agreed totally with the expected results from theoretical knowledge.

The induced emf establishes a current in the circuit which creates a magnetic field that opposes the original change in magnetic flux. When the parameters were modified in the programs, there were changes noted in the magnetic field, the inductance and the magnetic flux. Using the program to explore physics helps in simulating what cannot be seen with the naked eye hence giving a better understanding of the physical concepts. Some possible sources of errors could be the interference of the magnetic field by external factors hence causing erroneous results.