Question

Two long, parallel wires each carry the same current I = 2.00 A, pointing in opposite direction (see figure below). The two wires are 0.200 m apart. What is the total magnetic field at the point P midway between the wires?

Answer 1

Magnetic field due to long current carrying wire is

Но 0 27tr

where I is current in wire and r is distance from the wire to point.
As the current direction in one wire is opposite of other magentic field due to these wires sums up between them
therefore,
  B = $\mu$_oI₁/2$\pi$r_{1 +}$\mu$_oI₂/2$\pi$r₂
where r₁ r₂ are distance from the wires to point = 0.2m/2 = 0.1m
and
solving we get B = 2x$\mu$_oI/2$\pi$(0.1) as current I is same in both wires
=> B = 8 x 10^-6 T

Ho=4π x 10-7 T-rn / A

Answer 2

Assume that the wire on the right is wire 1 and that on the left is wire 2.

Also, choose the positive direction for the magnetic field to be out of the page

and negative into the page.

a)At the point halfway between the two points

=Bnet =-B1-B2 =-[$\mu o$ I1/2 pi r1 + $\mu o$ I2/2 pi r2]

                    =- (4 pi*10^-7 T.m/A)(2) /(2*pi* 0.1) =-4*10^-6 T

Bnet=4 $\mu$ T into the page

Answer 3

$B_{1}*2\prod*r=\mu _{o}*I_{enclosed}-->B_{1}=\mu _{o}*3.18$

Similarly $B_{2}*2\prod*r=\mu _{o}*I_{enclosed}-->B_{2}=\mu _{o}*3.18$

$So.. total ..Magenetic ..field=B_{1}+B_{2}=6.36*\mu _{o}=7.95*10^{-6}T$

Answer 4

This question can be done even without the figure only the direction cannot be acsertained..Since magnetic field vector is perpendicular to both current and direction vector, the magnetic field vector at the required point is perpendicular to the plane of paper that is it is either coming out of the plane or is directed inside the plane.Now by using Fleming's Right hand corkscrew rule,the magnetic at the mid point is added up due to the opposite direction of current in each wire.Therefore the total magnetic field at the mid point is:$2( \mu \times current\setminus (2 \times \pi \times distance))$

here the distance applied in formula is half of the distance between the wires

Now putting the values we get magnetic field as 8x10^-6Tesla

Answer 5

Answer) At point (a), midway between the wires, the field from
the top wire is