An infinite wire carrying current I1 runs along the z axis, another infinite wir

Question

An infinite wire carrying current I1 runs along the z axis, another infinite wire carrying current I2 runs parallel to the y axis, lies in the x-y plane and goes through the point (-L,0,0). (a) Find the magnetic field created by each wire at the point (0,2L,0) on the y axis. (b) Find the magnitude of the total magnetic field at this point.

[8 pts] An infinite wire carrying current runs along the z axis; the current flows from to z through the origin. Another infinite wire runs parallel to the y axis, lies in the r-y plane, and goes through the point (-L, 0,0). Current 21 flows through this wire, from y =-00 to y = +oo. Find the magnetic field created by each wire at the point (0,2L,0) on the y-axis. Find the magnitude of the total magnetic field at this point.

Explanation / Answer

field due to wire carrying current I1:

wire is along z axis .

using right hand thumb rule, field direction will be along -ve x axis.

field magnitude=mu*I/(2*pi*distance)

where mu=magnetic permeability=4*pi*10^(-7)

distance=2*L

so field magnitude=4*pi*10^(-7)*I1/(2*pi*2*L)=10^(-7)*I1/L

in vector notation field due to first wire=(10^(-7)*I1/L)*(-1,0,0)

field due to wire carrying current I1:

wire is parallel to y axis .

using right hand thumb rule, field direction will be along -ve z axis.

field magnitude=mu*I/(2*pi*distance)

where mu=magnetic permeability=4*pi*10^(-7)

perpendicular distance=L

so field magnitude=4*pi*10^(-7)*2*I1/(2*pi*L)=4*10^(-7)*I1/L

in vector notation field due to second wire=(4*10^(-7)*I1/L)*(0,0,-1)

total field=(10^(-7)*I1/L)*(-1,0,-4)

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