Physics 1402A/B Lecture Notes - Lecture 5: Cross Product

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harlequinbadger850

30 Dec 2018

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Lecture 5 notes 2 - parallel wires interactions. So, we now know that wires carrying current in a magnetic field will experience a force because of the impact of the magnetic field on the moving charged particles. We also know that the wire carrying a current will generate a magnetic field which can be measured by the biot-savart law. What is the impact of each field on the other. Let"s explore this concept a little further in this section of the lecture. Recall that the magnetic field proceed by current i1 is: where d is the distance from the wire in any direction, and the direction of this b field is given by a rhr. Well, if we have a setup of two parallel wires that are close to each other like below. Well we prefaced earlier that we know that it experiences a force! Thus, each wire will exert a force on the other.

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3. Shown below(screen shot at bottom) are two wires 100cm apart,the left carrying a current of 5A out of the page and the right acurrent of 10A into the page. The point P is midway between thewires.

(a) Calculate the magnetic field at P due to the left wire,expressing your answer in terms of the unit vectors i,j,k.
(b) Calculate the magnetic field at P due to the right wire (againexpress answer in terms of i,j,k).
(c) Calculate the total magnetic field at P due to bothwires.
(d) Draw an arrow at Q, which is vertically above P, showing theapproximate direction of the total magnetic field there. (You willget full credit if arrow is in the right quadrant).
(e) The magnetic field vanishes somewhere on the line joining thetwo wires. Where does this happen: to the left of 5A wire, inbetween the two wires or to the right of the 10A wire?
(f) As a followup to (e), calculate the exact place on the linejoining the wires where the magnetic field vanishes.
(g) A long wire is placed at P, parallel to the other two wires,and carrying a current of 3A out of the page. Calculate the forceexperienced by a 1cm portion of this wire, expressing your answerin terms of the unit vectors i,j,k.

Suppose you need to find the magnetic field near the intersection of two long straight current-carrying wires. Assume that one wire lies directly on the top of the other. Let the intersection of the wires be the origin of a coordinate system and let the point of interest, which is in the same plane, have coordinates (x,y). Recall that the magnetic field is a vector, having both a magnitude and direction.

a. What is the direction of magnetic field B₁ due to current I₁?

b. What is the direction of magnetic field B₂ due to current I₂? Explain

c. What are the only two possible directions for the net magnetic field at this point?

blueotter787

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.

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.

BM=

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Physics 1402A/B Lecture Notes - Lecture 5: Cross Product

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