Question
Two infinitely long straight wires lie in the xy-plane along the lines x = ±R. The wire located at x = +R carries a constant current I1 and the wire located at x = –R carries a constant current I2. A circular loop of radius R is suspended with its centre at (0, 0, ) and in a plane parallel to the xy-plane. This loop carries a constant current I in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the + direction. Which of the following statements regarding the magnetic field is (are) true ?
Options
If I1 = I2, then r cannot be equal to zero at the origin (0, 0, 0)
If I1 > 0 and I2 < 0, then can be equal to zero at the origin (0, 0, 0)
If I1 < 0 and I2 > 0, then can be equal to zero at the origin (0, 0, 0)
If I1 = I2, then the z-component of the magnetic field at the centre of the loop is
Solution
(A) At origin, = 0 due to two wires if I1 = I2, hence(net ) net at origin is equal to due to ring, which is non-zero.
(B) If I1 > 0 and I2 < 0, at origin due to wires will be along + direction and due to ring is along - direction and hence can be zero at origin.
(C) If I1 < 0 and I2 > 0, at origin due to wires is along - and also along - due to ring, hence cannot be zero.
(D)
At centre of ring, due to wires is along x-axis
hence z-component is only because of ring which
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