# Magnetic Field Due to Two Parallel Wires

## Homework Statement

A long, straight wire carries a current of 1.7 A in the +z direction and lies along the line x = –3.0 cm, y = 0. A second such wire carries a current of 1.7 A in the +z direction and lies along the line x = +3.0 cm, y = 0, as shown in Figure. Find the magnetic field at a point P on the y axis at y = 6.0 cm.

## The Attempt at a Solution

I understood why BL = BR
In my textbook, the solution says that vector B is the vector sum of vector BL and vector BR.

I don't understand this:

It says vector B = -2BL cos (theta) i ( in the -x direction)

i is the unit vector here

I have no idea where does the -2BL cos (theta) come from!

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What is the magnetic field a distance d from a current carrying wire? Can you exploit the symmetry of the situation?

Gokul43201
Staff Emeritus
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## Homework Statement

A long, straight wire carries a current of 1.7 A in the +z direction and lies along the line x = –3.0 cm, y = 0. A second such wire carries a current of 1.7 A in the +z direction and lies along the line x = +3.0 cm, y = 0, as shown in Figure. Find the magnetic field at a point P on the y axis at y = 6.0 cm.

## Homework Equations

Are there no relevant equations?

## The Attempt at a Solution

I understood why BL = BR
In my textbook, the solution says that vector B is the vector sum of vector BL and vector BR.

I don't understand this:

It says vector B = -2BL cos (theta) i ( in the -x direction)

i is the unit vector here

I have no idea where does the -2BL cos (theta) come from!
This is not an attempt at a solution. This is merely trying to read and understand the given solution. You will do better if you try to solve it by yourself, starting by drawing a figure showing the BL and BR vectors.