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 2.0 in the negative y-direction.

What is the magnitude of the magnetic field at the point (x=-7.0cm, y=5.3cm)? 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

magnetic field due to a long insulated wire at a distance of r is,

B=uo*i/(2pi*r)

here,

given,

point P(x,y)=(-7cm, 5.3cm)

field due to first wire which along x axis and current i=7.7 A

B1=uo*i/(2pi*y)

B1=4pi*10^-7*7.7/(2pi*5.3*10^-2)

B1=2.91*10^-5 T ( +z direction )

and

field due to second wire which along y axis and current i=2 A

B2=uo*i/(2pi*x)

B2=4pi*10^-7*2/(2pi*7*10^-2)

B2=5.71*10^-6 T ( -z direction )

net magnetic field is,

B=B1-B2

B=(2.91*10^-5-5.71*10^-6)

B=2.34 *10^-5 T

B=23.4*10^-6 T

B=23.4 uT (+z direction)

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