# C12B 2011 Problem 23Finding Zero Net Magnetic Field Points in Crossed Wires

• HoneyDeeLite
In summary: This can be found by considering the right hand rule and the direction of the currents. In summary, the net magnetic field will be zero at points where the fields due to the two currents are equal in magnitude and opposite in direction. These points can be found by considering the regions where the fields are pointing in opposite directions and finding the condition for equal magnitudes.
HoneyDeeLite

## Homework Statement

Two very long fixed wires cross each other at right angles. They do not touch but are
close to each other. Equal currents flow in each wire in the directions shown below.
Indicated the locus of points where the net magnetic field is zero.

(I2)
^
|
|
|
|
------------------------> (I1)
|
|

B = m0I/2pir

## The Attempt at a Solution

I know from the right hand rule that the magnetic field due to I1 will curl around towards me (out of the page) on top of the wire and point away from me (into the page) when directly below the wire.
The magnetic field due to I2 will point into the page when to the right of the wire and out of the page when to the left of the wire.
But it seems that the directions of the two fields will always be perpendicular to each other and thus never cancel out. How can there be a locus of points where the net magnetic field is 0?

I am not sure why you think the fields will be mutually perpendicular since they both go into and out of the plane (ie. the plane formed by the wires).

What you want to find are points where the fields are equal in magnitude and opposite in direction.

First, in what regions will the fields be pointing in opposite directions? Then determine what condition must be satisfied for the magnitudes to be equal. Find the points in those regions where the condition is satisfied.

AM

## 1. What is a magnetic field?

A magnetic field is a force field that surrounds a magnet or a moving electric charge. It is created by the movement of charged particles, such as electrons, and is characterized by its direction and strength.

## 2. How are magnetic fields produced by wires?

Magnetic fields are produced by wires when an electric current flows through them. The flow of electrons creates a circular magnetic field around the wire, with the direction of the field determined by the direction of the current.

## 3. Can magnetic fields from wires be harmful?

In general, the magnetic fields produced by wires are not harmful to humans. However, extremely strong magnetic fields, such as those found in MRI machines, can have adverse effects on the body. It is important to follow safety guidelines and limit exposure to high magnetic fields.

## 4. How do magnetic fields from wires affect other objects?

Magnetic fields from wires can affect other objects by exerting a force on them. This force can be attractive or repulsive, depending on the orientation of the objects and the direction of the magnetic field. Magnetic fields can also induce electric currents in nearby conductive materials.

## 5. How are magnetic fields from wires used in everyday life?

Magnetic fields from wires have many practical applications in everyday life. They are used in electric motors, generators, and transformers, as well as in various electronic devices. Magnetic fields are also used in magnetic levitation technology, which allows for the creation of high-speed trains and other forms of transportation.

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