Question

Two straight infinitely long and thin parallel wires are spaced 0.1 m apart and carry a current of 10 ampere each. Find the magnetic field at a point distant 0.1 m from both wires in the two cases when the currents are in the :
1) Same and 2) Opposite direction.

Answer 1

We have,

$D=0.1m$ apart

$I=10A$

Since the point P is at the equal distance for both wires A and B the distance between the wire is equal to

the point P,

$B_a=B_b=B$

$B=\frac{{\mu }_{0}2I}{4\pi d}={10}^{-7}\times \frac{2\times 10}{0.1}$

$2\times {10}^{-5}$

AS the magnetic lines of force of current curriying wire conccentric. So $B_a$ will be perpendicular to AP

and $B_b$ is perpendicular to AP.

a)If current are in same direction,

Then $B_a$ and $B_b$ make an angle $\frac{\pi }{3}$

Therefore, $B=2Bcos{60}^0=2\sqrt{3}\times {10}^{-5}T$ Along negative axis.

b) If current are in the oposite direction,

Then $B_a$ and $B_b$ will make an angle $\frac{2\pi }{3}$

$B=2Bcos\frac{2\pi }{3}=2\times {10}^{-5}T$