Which one of the following options represents the magnetic field vecB at O due to the current flowing in the given wire segments lying on the x y plane?

Question

Which one of the following options represents the magnetic field vecB at O due to the current flowing in the given wire segments lying on the x y plane? (A)  vecB=(-μ0 I/L)((3/2)+(1/4 √2 π)) hatk (B)  vecB=-(μ0 I/L)((3/2)+(1/2 √2 π)) hatk (C)  vecB=(-μ0 I/L)(1+(1/4 √2 π)) hatk (D)  vecB=(-μ0 I/L)(1+(1/4 π)) hatk

Tardigrade Admin · Accepted Answer

B =(μ0 I /4 π L ) sin 45°(- hat k )+(μ0 I π/4 π ( L )2)(- hat k )+(μ0 I /4 π ( L )4) × (π/2)(- hat k )

Q. Which one of the following options represents the magnetic field $B$ at $O$ due to the current flowing in the given wire segments lying on the $x y$ plane?

$B = \frac{- μ _{0} I}{L} (\frac{3}{2} + \frac{1}{4 2 π}) \hat{k}$

$B = - \frac{μ _{0} I}{L} (\frac{3}{2} + \frac{1}{2 2 π}) \hat{k}$

$B = \frac{- μ _{0} I}{L} (1 + \frac{1}{4 2 π}) \hat{k}$

$B = \frac{- μ _{0} I}{L} (1 + \frac{1}{4 π}) \hat{k}$

$B = \frac{μ _{0} I}{4 π L} sin 4 5^{\circ} (- \hat{k}) + \frac{μ _{0} I π}{4 π \frac{L}{2}} (- \hat{k}) + \frac{μ _{0} I}{4 π \frac{L}{4}} \times \frac{π}{2} (- \hat{k})$

Q. Which one of the following options represents the magnetic field B at O due to the current flowing in the given wire segments lying on the xy plane?

B=L−μ0​I​(23​+42​π1​)k^

B=−Lμ0​I​(23​+22​π1​)k^

B=L−μ0​I​(1+42​π1​)k^

B=L−μ0​I​(1+4π1​)k^