Two very long current carrying wires A and B carrying current $I_{0}$ (along z-axis) are placed at $(- a, 0)$ and $(a, 0)$ as shown. Find the value of magnetic field at $(0, a)$

Question

Smart Achievers · Accepted Answer

(2)

For infinitely long wire $B = \frac{μ_{0} I_{0}}{2 π r}, r = a \sqrt{2}, B_{res} = \sqrt{2} B$

Solution

Q.
Two very long current carrying wires A and B carrying current $I_{0}$ (along z-axis) are placed at $(- a, 0)$ and $(a, 0)$ as shown. Find the value of magnetic field at $(0, a)$

1 $\frac{μ_{0} I_{0}}{\sqrt{2} π a}$

2 $\frac{μ_{0} I_{0}}{2 π a}$

3 $\frac{μ_{0} I_{0}}{4 π a}$

4 $\frac{μ_{0} I_{0}}{2 \sqrt{2} π a}$

Ans.
(2)

For infinitely long wire $B = \frac{μ_{0} I_{0}}{2 π r}, r = a \sqrt{2}, B_{res} = \sqrt{2} B$

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Solution

Q. Two very long current carrying wires A and B carrying current I0 (along z-axis) are placed at (-a,0) and (a,0) as shown. Find the value of magnetic field at (0,a)

1 μ0I02πa

2 μ0I02πa

3 μ0I04πa

4 μ0I022πa

Ans. (2) For infinitely long wire B=μ0I02πr, r=a2, Bres=2B