Question

Two straight infinitely long and thin parallel wires are spaced 0.1 m apart and carry a current of 10A each. Find the magnetic field at a point distant 0.1 m from both wires when the currents are in the same direction.

• A. $2\sqrt{3}\times10^{-5}\,T$
• B. $2\times10^{-5}\,T$
• C. $4\times10^{-5}\,T$
• D. $Zero\,T$

Answer 1

Answer: (A)

$2\sqrt{3}\times10^{-5}\,T$

Answer 2

The given situation may be as shown in the diagram $\therefore$ Magnetic field, $B_A = B_B = \frac{\mu_0}{4\pi} \frac{2I}{a} = \frac{10^{-7} \times 2 \times 10}{0.1} = 2 \times 10^{-5}$ T As lines of force for current carrying wires A and B encircle them so BA is perpendicular to AP and $B_B$ is perpendicular to BP. Angle between these forces is $60^{\circ}$. $\therefore$ $B_R = 2(B_A \, cos \, 30) = 2 \left( 2 \times 10^{-5} \times \frac{\sqrt{3}}{2} \right)$