JEE Main 2021 · 18 March · morning · Single correct · +4 / −1
A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.
- (a) Loop assumes circular shape with its plane normal to the field.
- (b) Loop assumes circular shape with its plane parallel to the field.
- (c) Wire gets stretched to become straight.
- (d) Shape of the loop remains unchanged.
Answer and solution
Answer (a) Loop assumes circular shape with its plane normal to the field.
Solution
Physics sir · 4 steps
A flexible current loop settles where its energy is lowest, and that fixes both its shape and its orientation.
- Energy of a loop. A current loop behaves like a magnetic dipole with moment m = IA, where A is the area it encloses. Its energy in a uniform field depends on the angle θ between m⃗ and B⃗.
U = -mB cos θ = -IAB cos θ
- Orientation. The torque τ⃗ = m⃗ × B⃗ turns the loop until θ = 0, which gives the lowest U. Then m⃗ points along B⃗, so the plane of the loop is normal to the field.
- Shape. With θ = 0, every element feels I dl⃗ × B⃗ pointing outward in the plane, so the wire pushes out until A is as large as possible. For a fixed length of wire, the largest enclosed area is a circle.
- So. The loop becomes circular with its plane normal to the field, which is option (a).
The idea to keep. A current loop in a field always tries to maximise the flux through it. It turns its plane normal to B⃗, and if it is flexible, it also opens out to the largest area, a circle.
Answer from the NTA final answer key. Solution by PrepWiser.