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in Physics by (69.2k points)

A uniform constant magnetic field Vector B is directed at an angle of 45º to the X-ax is in X –Y plane. PQRS is a rigid square wire frame carrying a steady current I0 , with its centre at the origin O.At time t =0, the frame is at rest in the position shown in the figure with its sides parallel to X and Y axes. Each side of the frame is of mass M and length L.

(a) What is the torque Vector τ about O acting on the frame due to the magnetic field ?

(b) Find the angle by which the frame rotates under the action of this torque in a short interval of time Δt, and the axis about which this rotation occurs(Δt is so short that any variation in the torque during this interval may be neglected). Given : the moment of inertia of the frame about an axis through its centre perpendicular to its plane is

1 Answer

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by (69.7k points)
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Best answer

Magnetic moment of the loop, 

Magnetic Field,

(a) Torque acting on the loop,

(b) Axis of rotation coincides with the torque and since torque is in j - i direction or parallel to Q S.Therefore, the loop will rotate about an axis passing through Q and S as shown along-side :

Angular acceleration,

Where I = moment of inertia of loop about Q S.

(From theorem of perpendicular axis) 

∴ Angle by which the frame rotates in time Δt is

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