A Square Coil of Edge L and with N Turns Carries a Current I. It is Kept on a Smooth Horizontal Plate. a Uniform Magnetic Field B Exists Parallel to an Edge. the - Physics

Sum

A square coil of edge l and with n turns carries a current i. It is kept on a smooth horizontal plate. A uniform magnetic field B exists parallel to an edge. The total mass of the coil is M. What should be the minimum value of B for which the coil will start tipping over?

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Solution

Given:
Number of turns in the coil = n
Edge of the square loop = l
Magnetic field intensity = B
Magnitude of current = i
Angle between area vector and magnetic field, θ = 90°
Torque acting on the coil due to magnetic field,
τ = niABsinθ
Here, A is the area of the coil.
`τ = n"if"Bsin90^circ`
Torque produced due to weight, τweight =
`(mgl)/2`
For the coil to start tipping over,
τ ≥ τweight
For minimum value of B,
τ = τweight
`⇒ nil^2B =(mg)/l`
`⇒ B = (MG)/(2nil)`