(a) Calculate the y -components of the net magneticfield in the following places

Question

(a) Calculate the y-components of the net magneticfield in the following places: x1 = -12.5 cm,x2 = 5 cm, and x3 = 20 cm.(The x- and z-components of the B-field arezero.)

B(x1)y = T    *
0   OK

B(x2)y = T    *
1.45E-4   OK

B(x3)y = T     *
0   OK

HELP:  There are two ways to proceed.(1) Observe that the currents have planar symmetry. This allows thedirection of the magnetic field everywhere to bedetermined by a symmetry argument and the magnitude of theB-field to be determined everywhere by (repeated) application ofAmpere's law. (2) Use superposition; namely add the B-field fromthe left infinite current sheet (see textbook or lecture notes) tothat generated by the right infinite current sheet. This lattermethod is analogous to the use of superposition to find the E-fieldcreated by two parallel, infinite sheets of electric charge. As inthe E-field case, superposition is the easier route, and sosuperposition is recommended here as well.

(b) Suppose the above configuration of currents is unchangedexcept that the direction of the current IR isreversed so that now IR also flows in the+z direction (the magnitude remains the same). Calculatethe y-components of the net magnetic field now at the samepositions as in part (a).

B(x1)y = T    *
-1.45E-4   OK

B(x2)y = T    *
0   OK

B(x3)y =     *
1.45E-4   OK

HELP:  Use superposition again, asyou did in the previous part.
HELP:  Simple addition is all that'srequired. Can you identify the analogous electric fieldproblem?

(c) Return to the configuration of part (a).Suppose you want to have the region 0 < x <a able to confine electrons (e = 1.60 x10-19 C, m = 9.11 x 10-31 kg) thathave been accelerated from rest through a 51 V electrostaticpotential. If the electrons are to be stacked in circular orbitsparallel to the x-z plane with centers on theplane x = a/2, what is the minimumcurrent per wire required if IL andIR are equal in magnitude but opposite indirection?

IL = A    

HELP:  This builds on the previoushomework set and associated lecture notes and text material. First,find an algebraic expression for the radius R of anelectron's circular orbit in a spatially uniform B-field.
HELP:  What's the radius of the largestcircular orbit that can be fitted into the space between thecurrent sheets? (Neglect the thickness of the current sheetsthemselves.) Combine this value with your (algebraic result) frompart (a), and the radius of the largest possible orbit to solve forthe requested value of the current.

Two infinite sheets of current flow parallel to they-z plane. The left-hand sheet, which intersectsthe x-axis at x = 0, consists of an infinitearray of wires parallel to the z-axis with a densityn = 960 wires/m and a current per wire ofIL = 0.12 A in the +z direction. Theright-hand sheet, which intersects the x-axis atx = a = 10 cm, is identical to the left-handsheet, except that it has a current per wire ofIR = 0.12 A in the -z direction.

Explanation / Answer

anyone have any clue how to solve the last question?

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