Magnetic Effects & Magnetism

JEE Main level, single correct, medium

82 of 276

Question 82 of 276

As shown in the figure, two infinitely long, identical wires are bent by 90o{90}^{o} and placed in such a way that the segments LPLP and QMQM are along the xx - axis, while segments PSPS and QNQN are parallel to the yy - axis. If OP=OQ=4cm,OP=OQ=4cm, and the magnitude of the magnetic field at OO is 10−4T,{10}^{-4}T, and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at OO will be (μ0=4π×10−7NA−2):\left({\mu }_{0}=4\pi \times {10}^{-7}N{A}^{-2}\right):

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Answer: (A) 20A,20A, perpendicular into the page

As we know that the magnetic field due to a infinite wire at a distance of d is given as
B=(μ0i4πd)B=\left(\dfrac{{\mu }_{0}i}{4\pi d}\right)
but there are two wires so that the net magnetic field is given as

B=2(μ0i4πd)B=2\left(\dfrac{{\mu }_{0}i}{4\pi d}\right)

10−4=24π×10−7×i4π×(4100){10}^{-4}=2\dfrac{4\pi \times {10}^{-7}\times i}{4\pi \times \left(\dfrac{4}{100}\right)}

i=20Ai=20A

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