# 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.

In the order asked:

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

abovethe wire, the magnetic field is pointingout of the plane,toward you.

#:.B=5.7xx10^-7"T"# out of the planeFor 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

belowthe wire, the magnetic field is pointinginto the plane,away from you.

#:.B=8.17xx10^-7"T"# into the planeFor 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 planeFor 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

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To calculate the magnetic field at a distance ( r ) from a long straight current-carrying wire, you can use the formula:

[ B = \frac{{\mu_0 \cdot I}}{{2\pi \cdot r}} ]

where:

- ( B ) is the magnetic field in teslas (T),
- ( \mu_0 ) is the permeability of free space ((4\pi \times 10^{-7} , \text{T m/A})),
- ( I ) is the current in the wire in amperes (A),
- ( r ) is the distance from the wire in meters (m).

You'll need to convert all distances to meters before calculating.

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*Answer from HIX Tutor*

*When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.*

*When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.*

*When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.*

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