Two infinitely long string wires are arranged perpendicular to each other and are in mutually perpendicular planes as shown in figure. If $I_{1} = 2 A$ along the y-axis and $I_{2} = 3 A$ along negative z-axis and AP=AB=1cm The magnetic induction $\vec{B}$ at point p is ;

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$(4 \times 10^{- 5} T) \overset{\land}{j} + (3 \times 10^{- 5} T) \overset{\land}{k}$

$(- 3 \times 10^{- 5} T) \overset{\land}{j} + (4 \times 10^{- 5} T) \overset{\land}{k}$

$(3 \times 10^{- 5} T) \overset{\land}{j} + (4 \times 10^{- 5} T) \overset{\land}{k}$

$(3 \times 10^{- 5} T) \overset{\land}{j} + (- 4 \times 10^{- 5} T) \overset{\land}{k}$

answer is B.

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Detailed Solution

Magnetic induction at point p due current $I_{1}$ is given as

$\vec{B_{1}} = \frac{μ_{0} I}{2 π (A P)} \overset{\land}{K} = \frac{4 π \times 10^{- 7} \times 2}{2 π \times 1 \times 10^{- 2}} \overset{\land}{K} = (4 \times 10^{- 5} T) \overset{\land}{K}$

Magnetic induction at point p due current $I_{2}$ is given as

$\vec{B_{2}} = \frac{μ_{0} I_{2}}{2 π (B P)} \overset{\land}{j} = \frac{4 π \times 10^{- 7} \times 3}{2 π \times 2 \times 10^{- 2}} \overset{\land}{j} = (3 \times 10^{- 5} T) \overset{\land}{j}$