A coil, in the shape of an equilateral triangle of side l , is suspended between two pole pieces of a permanent magnet, such that the magnetic field B is in the plane of the coil. If due to current I in the triangle, a torque τ acts on it, the side l of the triangle is

Question

A coil, in the shape of an equilateral triangle of side l , is suspended between two pole pieces of a permanent magnet, such that the magnetic field B is in the plane of the coil. If due to current I in the triangle, a torque τ acts on it, the side l of the triangle is (A) 2((τ/√3 B I))(1/2)  (B) (2/√3)((τ/B I)) (C) 2((τ/B I))(1/2) (D) (1/√3)(τ/B I)

Tardigrade Admin · Accepted Answer

Torque acting on an equilateral triangle in a magnetic field

B

is

τ = I A B s in θ

Area of

Δ L MN : A = \frac{3}{4} l^{2}

and

θ = 9 0^{o}

Substituting the given values in the expression for torque, we have
Solution

τ = I \times \frac{3}{4} l^{2} B s in 9 0^{\circ} = \frac{3}{4} I l^{2} B

∴ l = 2 (\frac{τ}{3 B I})^{\frac{1}{2}}

Q. A coil, in the shape of an equilateral triangle of side $l$ , is suspended between two pole pieces of a permanent magnet, such that the magnetic field $B$ is in the plane of the coil. If due to current $I$ in the triangle, a torque $τ$ acts on it, the side $l$ of the triangle is

$2 (\frac{τ}{3 B I})^{\frac{1}{2}}$

$\frac{2}{3} (\frac{τ}{B I})$

$2 (\frac{τ}{B I})^{\frac{1}{2}}$

$\frac{1}{3} \frac{τ}{B I}$

Q. A coil, in the shape of an equilateral triangle of side l , is suspended between two pole pieces of a permanent magnet, such that the magnetic field B is in the plane of the coil. If due to current I in the triangle, a torque τ acts on it, the side l of the triangle is

2(3​BIτ​)21​

3​2​(BIτ​)

2(BIτ​)21​

3​1​BIτ​

Torque acting on an equilateral triangle in a magnetic field B is τ=IABsinθ Area of ΔLMN:A=43​​l2 and θ=90o Substituting the given values in the expression for torque, we have τ=I×43​​l2Bsin90∘=43​​Il2B ∴l=2(3​BIτ​)21​

Q. A coil, in the shape of an equilateral triangle of side $l$ , is suspended between two pole pieces of a permanent magnet, such that the magnetic field $B$ is in the plane of the coil. If due to current $I$ in the triangle, a torque $τ$ acts on it, the side $l$ of the triangle is

$2 (\frac{τ}{3 B I})^{\frac{1}{2}}$

$\frac{2}{3} (\frac{τ}{B I})$

$2 (\frac{τ}{B I})^{\frac{1}{2}}$

$\frac{1}{3} \frac{τ}{B I}$