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.
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 the permeability of free spaceRight 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 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 below the wire, the magnetic field is pointing into 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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