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A non - conducting sphere has mass of100 gand radius 20 cm . Aflat compact coil of wire with turns 5 iswrapped tightly around it with each turns concentric with the sphere. This sphere is placed on an inclined plane such that plane of coil is parallel to the inclined plane. A uniform magnetic field of 0.5 T exists in the region in vertically upwards direction. Compute the current I required to rest the sphere in equilibrium.(##SUR_PHY_XII_V01_C03_E04_005_Q01##) |
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Answer» Solution :The sphere is in translational equilibrium , thus`f_(s)- mgsin theta ` = 0 ….(1) The sphere is in rotational equilibrium . If torques are taken about the centre of the sphere, the magnetic field produces a clockwise torque of magnitude i.e`tau = mBsinq [mu = NIA]` The frictional force `(f_(s))` produces a anticlockwise torque of magnitude `tau = f_(s)R`, where R is theradius of the sphere. Thus ` f_(s) R - mB SIN theta = 0 ` .....(2) From (1) and (2)[i.e `f_(s)= mgsin theta ` substituting in (2)]mg `sin theta. R - mu B sin theta mgR= mu B ` Substituting ` mu ` mgR = NIAB ` I = "mgR"/"NBA" ` [where A is the area of the sphere ` A = pi R^(2) ` ] ` :.I = "mg"/(pi"RBN")` Given : mass of thesphere` mu= 100 g = 100xx 10^(-3) kg ` Radius of the sphere` R = 20 cm= 20XX 10 ^(-2) m ` No. of turns of wire wrapped` N = 5` Magnetic field ` B = 0.5 ` T Current required to rest the sphere in equilibrium` I = ? ` `I = (100 xx 10^(-3) xx cancel10^(2))/(pi xx cancel5 xx 20 xx 10^(-2) xx 0.5) ` ` I = 2/pi A ` |
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