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.

1 Answer
Aug 10, 2017

Answer:

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:

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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