10. Current is passed through this flexible loop of wire, which is placed on a
frictionless insulating table. What will be the resulting effect on the shape of the wire?
a. The wire will expand to form a circular loop
b. The wire will bunch up further
c. The wire will lift off the table
d. There will be no effect
The correct answer is (a) The wire will expand to form a circular loop.
Introduction
When current flows in a flexible loop of wire lying on a frictionless insulating table, magnetic forces act on every tiny segment of the wire. These forces rearrange the loop into the most stable, lowest‑energy shape: a circle that encloses maximum area for the given length of wire.
Concept: Why the loop becomes circular
Each element dℓ⃗ of a current‑carrying conductor in a magnetic field experiences a force dF⃗=I dℓ⃗×B⃗. For a loop, these forces act tangentially and symmetrically so that the net effect is to pull the wire outwards, increasing the enclosed area until the loop becomes circular. A circle gives uniform tension everywhere along the wire, so it is the configuration of mechanical and magnetic equilibrium.
Option (a): The wire will expand to form a circular loop
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Magnetic forces between different current elements are repulsive along the inside of the loop, so each segment is pulled away from the centre.
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Because the table is frictionless and the wire is flexible, nothing resists this motion, so the irregular loop smooths out and expands until it becomes a circle, making option (a) correct.
Option (b): The wire will bunch up further
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Bunching up would require net inward forces compressing the wire, but the self‑interaction of the current produces outward forces that try to stretch the loop instead.
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Therefore the loop does the opposite of bunching; it spreads out to maximize area, so option (b) is incorrect.
Option (c): The wire will lift off the table
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The magnetic forces on opposite segments largely lie in the plane of the loop, producing tension rather than a net vertical force.
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Since the table is insulating but not exerting any vertical magnetic force, there is no reason for the center of mass of the loop to accelerate perpendicular to the table, so option (c) is incorrect.
Option (d): There will be no effect
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The presence of current guarantees magnetic forces between different parts of the loop, and these forces are unbalanced when the shape is irregular.
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With both flexibility and zero friction, even small forces are enough to change the shape, so the loop cannot remain unchanged, making option (d) wrong.
