Two very long, thin straight wires lie along the X-axis and Y-axis, each carrying equal current away from the origin O. Lines AB and CD pass through O at 45° to the axes, as shown in the figure (with A, B, C, D in alternate quadrants). On which line is the net magnetic field due to the two wires zero everywhere?

PhysicsMediumHigh School (11–12)jee-main

The magnetic field from a straight current-carrying wire at a point depends on the perpendicular distance from the wire and the angles subtended by the ends of the wire. On the diagonal lines, by symmetry the perpendicular distances from the two wires are equal, making the contributions from both wires cancel exactly at every point along that line.

Two very long, thin straight wires lie along the X-axis and Y-axis, each carrying equal current away from the origin $O$ . Lines $AB$ and $CD$ pass through $O$ at $45°$ to the axes, as shown in the figure (with $A$ , $B$ , $C$ , $D$ in alternate quadrants). On which line is the net magnetic field due to the two wires zero everywhere?

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← An infinitely long conductor PQR is bent to form a right angle, with current I flowing through the path PQ and QR. The magnetic field due to this current at a point M (located perpendicular to PQ at the bend) is H₁. Now another infinitely long straight conductor QS is connected at Q (collinear with PQ, extending in the opposite direction), so that the current becomes I/2 in QR as well as in QS, while the current in PQ remains unchanged at I. The magnetic field at M is now H₂. What is the ratio H₁:H₂?A positively charged particle moves in the xy-plane, initially along the x-axis. Beyond a point P, due to the presence of electric and/or magnetic fields, its path curves and is found to be non-circular (though still confined to the xy-plane). Which combination of fields is consistent with this observation? →

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