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.

Question

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.

Infinity Learn · Accepted Answer

Consider a small element , at point P, of length $d l$ and mass $d m = \frac{m}{2 π R} d l$

Magnetic force on this element is given by

$d F = i d l B \sin θ [w h e r e θ i s t h e a n g l e b e t w e e n \vec{d l} a t P a n d \vec{B}] \Rightarrow (d m) a = i d l B \sin θ \Rightarrow (\frac{m}{2 π R} d l) a = i d l B \sin θ \Rightarrow a = m 2 π R B \sin θ = (1) (2 π) (1) (5) (\frac{4}{5}) = 8 π m / s^{2}$

Magnetic force

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Magnetic force

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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.

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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