A coil in the shape of an equilateral triangle of side 115...

A coil in the shape of an equilateral triangle of side 115 suspended between the pole pieces of a permanent magnet such that $\mathrm{B}^{-}$ is in plane of the coil. If due to a current $\mathrm{I}$ in the triangle a torque $\tau$ acts on it, the side 1 of the triangle is (a) $(2 / \sqrt{3})(\tau / \mathrm{BI})^{1 / 2}$ (b) $(2 / 3)(\tau / B I)$ (c) $2[\tau /\{\sqrt{(} 3) \mathrm{BI}\}]^{1 / 2}$ (d) $(1 / \sqrt{3})(\tau / \mathrm{BI})$

A coil in the shape of an equilateral triangle of side 115 suspended between the pole pieces of a permanent magnet such that $\mathrm{B}^{-}$ is in plane of the coil. If due to a current $\mathrm{I}$ in the triangle a torque $\tau$ acts on it, the side 1 of the triangle is
(a) $(2 / \sqrt{3})(\tau / \mathrm{BI})^{1 / 2}$
(b) $(2 / 3)(\tau / B I)$
(c) $2[\tau /\{\sqrt{(} 3) \mathrm{BI}\}]^{1 / 2}$
(d) $(1 / \sqrt{3})(\tau / \mathrm{BI})$

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Key Concepts

Magnetic Torque on a Current Loop

A current-carrying loop in a magnetic field experiences a torque that tends to align its magnetic dipole moment with the external field. The torque is calculated using the cross product ? = ? × B, where ? is the magnetic dipole moment and B is the magnetic field. This relationship is essential in understanding how the loop interacts with the magnetic field and is particularly useful when evaluating the forces and resulting motions in magnetic systems.

Magnetic Dipole Moment

The magnetic dipole moment represents the strength and orientation of a current loop's magnetic field and is defined as ? = I × A, with I being the current and A the area of the loop. It plays a crucial role in quantifying how the loop responds to an external magnetic field, particularly in determining the magnitude of the torque it experiences.

Area of an Equilateral Triangle

Calculating the area of an equilateral triangle is vital in determining the magnetic dipole moment for a triangular coil. The area is given by A = (?3 / 4) × s², where s is the side length of the triangle. This geometrical relationship allows one to relate the physical dimensions of the triangle to its overall magnetic properties when current flows through it.

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