A long insulated wire is stretched along the x-axis. A current of 7.7 A flows in

Question

A long insulated wire is stretched along the x-axis. A current of 7.7 A flows in this wire in the positive x-direction.

Another long insulated wire is stretched along the y-axis. It carries a current of 3.8 A in the negative y-direction.

What is the magnitude of the magnetic field at the point (x=4.2cm, y=3.8cm)? The answer may be given in the units of mT or uT.

The answer should be positive if the direction of the magnetic field is up (in the positive z-direction), and negative if the direction of the magnetic field is down.

Explanation / Answer

given,

current on x axis wire = 7.7 A

current on y axis wire = 3.8 A

distance of point from x axis = 3.8 cm

distance of point from y axis = 4.2 cm

magnetic field due to x axis wire = k * I / r

magnetic field due to x axis wire = 2 * 10^-7 * 7.7 / 0.038

magnetic field due to x axis wire = 0.00004052631 T

magnetic field due to y axis wire = 2 * 10^-7 * 3.8 / 0.042

magnetic field due to y axis wire = 0.00001809523 T

since thedirection of both the magnetic field is opposite

net magnetic field = 0.00004052631 - 0.00001809523

net magnetic field = 0.00002243108 T or 0.02243108 mT or 22.43108 uT

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