A pair of stationary and infinitely long bent wires are placed in the x-y plane as shown in figure. The wires carry currents of 10A each as shown. The segments L and M are along the x-axis. The segments P and Q are parallel to the y-axis such that OS = OR = 0.02m. Find magnitude and direction of the magnetic induction at the origin O.

Question

A pair of stationary and infinitely long bent wires are placed in the x-y plane as shown in figure. The wires carry currents of 10A each as shown. The segments L and M are along the x-axis. The segments P and Q are parallel to the y-axis such that OS = OR = 0.02m. Find magnitude and direction of the magnetic induction at the origin O. (A) 100 Wb m-2 vertically upward (B) 10-4 Wb m-2 vertically downward (C) 10-4 Wb m-2 vertically upward (D) 0.01 Wb m-2 vertically downward

Tardigrade Admin · Accepted Answer

Point O is along the segments L and M, so magnetic field due to them is zero. Point O is near the
end of conductors P and Q.

B_{R} = B_{p} + B_{Q} = \frac{μ _{0} I}{4 π RO} + \frac{μ _{0} I}{4 π SO} = \frac{μ _{0}}{4 π} (\frac{2 I}{d})

Using the given data,

B_{R} = 1 0^{- 7} \times \frac{2 \times 10}{0.02} = 1 0^{- 4} Wb m^{- 2}

, outside the sheet of paper.

$100 Wb m^{- 2}$ vertically upward

$1 0^{- 4} Wb m^{- 2}$ vertically downward

$1 0^{- 4} Wb m^{- 2}$ vertically upward

$0.01 Wb m^{- 2}$ vertically downward

100Wbm−2 vertically upward

10−4Wbm−2 vertically downward

10−4Wbm−2 vertically upward

0.01Wbm−2 vertically downward

Point O is along the segments L and M, so magnetic field due to them is zero. Point O is near the end of conductors P and Q. BR​=Bp​+BQ​=4πROμ0​I​+4πSOμ0​I​=4πμ0​​(d2I​) Using the given data, BR​=10−7×0.022×10​=10−4Wbm−2 , outside the sheet of paper.

$100 Wb m^{- 2}$ vertically upward

$1 0^{- 4} Wb m^{- 2}$ vertically downward

$1 0^{- 4} Wb m^{- 2}$ vertically upward

$0.01 Wb m^{- 2}$ vertically downward