Q.

Consider a metallic ring of radius 1m, mass 1kg, and carrying current 1A in a gravity free space in x-y plane with its center at origin as shown. If a uniform magnetic field 3i^+4j^T is applied, then instantaneous acceleration of point P(which is on the y-axis at the moment) is nπ   m/s2. Find n.

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answer is 8.

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Detailed Solution

Consider a small element , at point P, of length dl and mass dm=m2πRdlMagnetic force on this element is given bydF=idlBsinθ     where θ is the angle between dl→ at P and B→  ⇒dma=idlBsinθ ⇒m2πRdla=idlBsinθ ⇒a=m2πRBsinθ=12π1545=8π m/s2
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