Question

How would you calculate the magnetic field in the following places: 33cm to the north of the wire? 230mm to the south of the wire? 880μm below the wire? 0.18m above the wire?

A wire is traveling east to west through iron. A 940mA current is running through the wire going towards the east.

Answer 1

In the order asked: `B=5.7xx10^-7"T out of the plane, " 8.17xx10^-7"T into the plane, " 2.14xx10^-4"T into the plane, "1.04xx10^-6"T out of the plane"`

Explanation:

The magnetic field generated by a current-carrying wire is given by:

`B=(mu_oI)/(2pir)`

where `I` is the current through the wire, `r` is the distance from the wire to the specified point, and `mu_o` is a constant for the permeability of free space

Right hand rule to find direction of magnetic field:

We are given the following information:

• `|->I=940xx10^-3"A"`
• `|->mu_o=4pixx10^-7("T"*"m")/"A"`
• `|->r_1=0.33"m (north)"`
• `|->r_2=0.230"m (south)"`
• `|->r_3=880xx10^-6"m (south)"`
• `|->r_4=0.18"m (north)"`

For the first position, we have:

`B=(mu_oI)/(2pir_1)`

`=>=((4pixx10^-7("T"*"m")/"A")(940xx10^-3"A"))/(2pi(0.33"m"))`

`=>=5.7xx10^-7"T"`

By the right hand rule, for a point above the wire, the magnetic field is pointing out of the plane, toward you.

`:.B=5.7xx10^-7"T"` out of the plane

For the second position, we have:

`B=(mu_oI)/(2pir_2)`

`=>=((4pixx10^-7("T"*"m")/"A")(940xx10^-3"A"))/(2pi(0.230"m"))`

`=>=8.17xx10^-7"T"`

By the right hand rule, for a point below the wire, the magnetic field is pointing into the plane, away from you.

`:.B=8.17xx10^-7"T"` into the plane

For the third position, we have:

`B=(mu_oI)/(2pir_3)`

`=>=((4pixx10^-7("T"*"m")/"A")(940xx10^-3"A"))/(2pi(880xx10^-6"m"))`

`=>=2.14xx10^-4"T"`

`:.B=2.14xx10^-4"T"` into the plane

For the fourth position, we have:

`B=(mu_oI)/(2pir_4)`

`=>=((4pixx10^-7("T"*"m")/"A")(940xx10^-3"A"))/(2pi(0.18"m"))`

`=>=1.04xx10^-6"T"`

`:.B=1.04xx10^-6"T"` out of the plane