Student’s guide to maxwells’ equations. problem 4.1 Peeter Joot July 20, 2008

1 Problem is: Two parallel wires carry currents I1 and 2I1 in opposite directions. Use Amperes law to find the magnetic field at a point midway between the wires. Do this instead (visualizing the cross section through the wires) for N wires located at points Pk , with currents Ik .

Figure 1: Currents through parallel wires This is illustrated for two wires in figure 1.


1.1 Consider first just the magnetic field for one wire, temporarily putting the origin at the point of the current. Z

B · dl = µ0 I

At a point r from the local origin the tangent vector is obtained by rotation of the unit vector:      r xˆ yˆ r = yˆ yˆ exp xˆ yˆ log krk krk Thus the magnetic field at the point r due to this particular current is: B(r) =

µ0 I yˆ 2π krk

r krk

xˆ yˆ

Considering additional currents with the wire centers at points Pk , and measurement of the field at point R we have for each of those: r = R−P Thus the total field at point R is: µ0 yˆ B(R) = 2π


∑ k

Ik kR − Pk k

R − Pk kR − Pk k

xˆ yˆ (1)

Original problem.

For the problem as stated, put the origin between the two points with those two points on the x-axis. P1 = −xˆ d/2 P2 = xˆ d/2 Here R = 0, so r1 = R − P1 = xˆ d/2 and r2 = −xˆ d/2. With xˆ yˆ = i, this is:  µ0 yˆ  I1 (−xˆ )i + I2 xˆ i πd µ0 yˆ = (− I − 2I ) πd −3Iµ0 yˆ = πd

B (0) =

Here unit vectors exponentials were evaluated with the equivalent complex number manipulations: 2

(−1)i = x i log (−1) = log x iπ = log x exp (iπ ) = log x x = −1

(1) i = x i log (1) = log x 0 = log x x=1


Student's guide to maxwells' equations. problem 4.1

Jul 20, 2008 - Problem is: Two parallel wires carry currents I1 and 2I1 in opposite directions. Use.

75KB Sizes 2 Downloads 288 Views

Recommend Documents

Admission Guide for International Students
Admission Criteria p.11. V. Important Notes p.12. VI. Academic Programs for Bachelor's Degree p.16 ... Go to and fill out your online application form. ↓. Please make sure that the ... junior high, and hig

pdf-1837\louisiana-a-students-guide-to-localized-history-localized ...
Try one of the apps below to open or edit this item. pdf-1837\louisiana-a-students-guide-to-localized-history-localized-history-series-by-joe-gray-taylor.pdf.

A Quick Guide to Problem Solving - Taylor Consulting
A Quick Guide to Problem Solving | ..... 2) Subscribe to our free weekly email newsletter, and get new career development tools ... Set up corporate access to our rich blended learning environment, the Mind Tools Club.

Department of Crop Science, University of Calabar, P.M.B. 1115, Calabar,Nigeria ... Whoops! There was a problem loading this page. 41.pdf. 41.pdf. Open.

0780-01 -41
Chapter 0780-1-41 Tennessee Captive Insurance Companies is amended by ..... This Rule shall apply to any captive insurance company formed or licensed ...

Maxwell's Equations
Jan 9, 2017 - ϵr = 1.33, but at RF down to dc, it has n = 9. In Sec. 1.9, we discuss simple models of ..... The real and imaginary parts of ϵ(ω) characterize the refractive and absorptive properties of the material. ... exhibits strong absorption.

Maxwell's Equations
Jan 9, 2017 - The quantities ρ and J are the volume charge density and electric current density. (charge flux) of any ... The electric and magnetic flux densities D, B are related to the field intensities E, H via the so-called .... nonlinear effect