A wire of length L carries a charge λ per unit length. (a) Showthat the electric field at a point a distance R from the wire isgiven by:
Eperpendicular = (kλ/R)(sinθ2-sinθ2) andEparallel = -(kλ/R)(cosθ2-cosθ1),
where E perpendicular and E parallel are the components of Eperpendicular and parallel to the wire and θ1 andθ2 are the angles that the lines from the point to theends of the wire make with the perpendicular to the wire. (b) Findthe field when the point is equidistant from both ends. (c) Thesigns of angles θ1 and θ2 are indicated inthe figure.
A wire of length L carries a charge λ per unit length. (a) Showthat the electric field at a point a distance R from the wire isgiven by:
Eperpendicular = (kλ/R)(sinθ2-sinθ2) andEparallel = -(kλ/R)(cosθ2-cosθ1),
where E perpendicular and E parallel are the components of Eperpendicular and parallel to the wire and θ1 andθ2 are the angles that the lines from the point to theends of the wire make with the perpendicular to the wire. (b) Findthe field when the point is equidistant from both ends. (c) Thesigns of angles θ1 and θ2 are indicated inthe figure.
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In this problem, you will be asked to calculate the magnetic field due to a set of two wires with antiparallel currents as shown in the diagram (Figure 1) . Each of the wires carries a current of magnitude I. The current in wire 1 is directed out of the page and that in wire 2 is directed into the page. The distance between the wires is 2d. The x axis is perpendicular to the line connecting the wires and is equidistant from the wires.
As you answer the questions posed here, try to look for a pattern in your answers.
Part A
Which of the vectors best represents the direction of the magnetic field created at point K (see the diagram in the problem introduction) by wire 1 alone?
Enter the number of the vector with the appropriate direction.
Part B
Which of the vectors best represents the direction of the magnetic field created at point K by wire 2 alone?
Enter the number of the vector with the appropriate direction.
Part C
Which of these vectors best represents the direction of the net magnetic field created at point K by both wires?
Enter the number of the vector with the appropriate direction.
Part D
Point M is located a distance 2d from the midpoint between the two wires. Find the magnitude of the magnetic field B1M created at point M by wire 1.
Express your answer in terms of I, d, and appropriate constants.
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| B1M= |
Part E
Find the magnitude of the net magnetic field BM created at point M by both wires.
Express your answer in terms of I, d, and appropriate constants.
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| BM= |
