Two coaxial solenoids of different radius carry current I in the same direction. F₁ be the magnetic force on the inner solenoid due to the outer one and F₂ be the magnetic force on the outer solenoid due to the inner one. Then: (a) F₁ is radially in wards and F₂ = 0 (b) F₁ is radially outwards and F₂ = 0 (c) F₁ = F₂ = 0 (d) F₁ is radially inwards and F₂ is radially outards

Answer: (c). The field of the inner solenoid is zero outside it, so the outer solenoid feels no force: F₂ = 0. The outer solenoid's field inside is uniform and axial; on the inner coil's circular turns the forces I dl × B are radial and cancel around each turn. Net force F₁ = 0. So the answer is (c) F₁ = F₂ = 0.

Two coaxial solenoids of different radius carry current I in the same… | JEE Main 2015

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Two coaxial solenoids of different radius carry current $I$ in the same direction. $\vec{F_1}$ be the magnetic force on the inner solenoid due to the outer one and $\vec{F_2}$ be the magnetic force on the outer solenoid due to the inner one. Then:

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Answer: (c)

The field of the inner solenoid is zero outside it, so the outer solenoid feels no force: $\vec{F_2} = 0$ .
The outer solenoid's field inside is uniform and axial; on the inner coil's circular turns the forces $I\,d\vec{l} \times \vec{B}$ are radial and cancel around each turn.
Net force $\vec{F_1} = 0$ .
So the answer is (c) $\vec{F_1} = \vec{F_2} = 0$ .

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