Q. 58

# A square coil of edge ℓ having n turns carries a current i. It is kept on a smooth horizontal plate. A uniform magnetic field B exists in a direction 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?

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,

Where

B= applied magnetic field

A= area of rectangular loop

I = current flowing through coil

= angle between the area vector and magnetic field

Torque produced due to weight is

given by,

where m is the mass

g is the acceleration due to gravity

For the coil to start tipping towards downwards,

For minimum value of B,

From (1) and(2)

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