# 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?

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

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

##### 1 Answer

In the order asked:

#### 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 thepermeability 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.

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.

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"#

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"#