# A uniform, constant magnetic field B is directed at an angle of 45 to the x axis in the xy-plane. PQRS is s rigid, square wire frame carrying a steady current I 0 , with its centre at the origin O. At time t = 0, the frame is at rest n the position as shown in Figure, with its sides parallel to the x and y axes. Each side of the frame is of mass M and length L. (a) What is the torque 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 ∆t, and the axis about this rotation occurs. (∆t is so short that any variation in the torque during this interval may be neglected.) Give : the moment of inertia of the frame about an axis through its centre perpendicular to its plane is 4/3 ML 2

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A uniform, constant magnetic field B is directed at an angle of 45 to the x axis in the xy-plane. PQRS is s rigid, square wire frame carrying a steady current I_{0}, with its centre at the origin O. At time t = 0, the frame is at rest n the position as shown in Figure, with its sides parallel to the x and y axes. Each side of the frame is of mass M and length L.(a) What is the torque 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 ∆t, and the axis about this rotation occurs. (∆t is so short that any variation in the torque during this interval may be neglected.) Give : the moment of inertia of the frame about an axis through its centre perpendicular to its plane is 4/3 ML^{2}

_{0}, with its centre at the origin O. At time t = 0, the frame is at rest n the position as shown in Figure, with its sides parallel to the x and y axes. Each side of the frame is of mass M and length L.

^{2}

## 1 Answers

_{x}= B cos 45° = B / √2 and

_{y}= B sin 45° = B / √ 2

^{2}

_{0}L

^{2}B and is directed along line QS from Q to S.

_{QS}= 1 / 2 I

_{z}= 1/ 2 ( 4 / 3 ML

^{2}) = 2 / 3 ML

^{2}

_{0}L

^{2}B x 3 / 2ML

^{2}= 3 / 2 I

_{0}B / M

_{0}t + 1 / 2 αt

^{2}with ω

_{0}= 0, we have

^{2}= 1 / 2 (3I

_{0}B / 2M) (∆t)

^{2}

_{0}B / M (∆t)

^{2}

Deepak patra

askIITians Faculty