Question

The following diagram shows two parallel straight conductors carrying same current. Copy the diagram and draw the pattern of magnetic field lines around them showing their directions. What is the magnitude of magnetic field at a point X which is equidistace from conductors.

Answer 1

direction of magnetic field is given by $\textbf{\underline{Right-hand rule}}$. by using right- hand rule direction of magnetic field at X by left wire is out of the page (•) and direction of magnetic field at X by right wire is into the page (×) as shown in figure.

magnitude of magnetic is given by using $\textbf{Biot Savart law}$.

for infinite long wire,

magnitude of magnetic field is given by, $B=\frac{\mu_0I}{2\pi r}$

where, I is current through wire and r is the separation between wire and observations points.

so, magnetic field due to left wire at X, $B=\frac{\mu_0I}{2\pi d}\odot$

again, magnetic field due to right wire at X , $B=\frac{\mu_0I}{2\pi d}\otimes$

so, the net magnetic field at X = $B\odot+B\otimes$ = 0