- #1

cookiemnstr510510

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## Homework Statement

A) Three infinite, current-carrying wires are arranged as shown below. In terms of the given quantities, determine the magnitude and direction of the magnetic force per length acting upon wire 2. (Part A.jpg attached)

B) Three infinite, current-carrying wires are arranged as shown below in terms of the given quantities, determine the magnitude and direction of the magnetic force per length acting upon wire 5.(Part B.jpg attached)

## Homework Equations

B=(μ

_{0}I)/(2πd)

F=ILxB

## The Attempt at a Solution

A) Both wires 1 and 3 create a magnetic field at the location of wire 2.

Wire 1's magnetic field points straight upward in the j-hat direction.

Wire 3's magnetic field points at a -45° angle from the positive i-hat direction which is from left to right.

Using right hand rule:

F

_{1 on 2}is in the positive i-hat direction

and

F

_{3 on 2}is -45° from the negative i-hat direction

These forces are shown in (forces.jpg)

F

_{1on2}=I

_{2}LB

_{1}i-hat

B

_{1}=(μ

_{0}I

_{1})/(2πd)

therefore:

F

_{1on2}=(I

_{2}I

_{1}LB

_{1})/(2πd) i-hat

F

_{3 on 2}=I

_{2}LxB

_{2}= here is where I am stuck- when doing the cross product here is the θ the angle between both wires? I guess I am confusing the cross product we do for magnetic field and the one we do for forces..

Any help would be appreciated!