In figure, AB is a $$non-conducting$$ rod. Equal charges of magnitude q are fixed at various points on the rod as shown. The rod is rotated uniformly about an axis passing through O and perpendicular to its length such that linear speed of the end A or B of the rod is $$3$$ mis. Magnetic field at O is

Question

Infinity Learn · Accepted Answer

Since the rod is a rigid body, every point has same angular velocity ω$$=1$$  $$rad/s$$.For points at a distance of $$1$$ m, $$v1$$ $$=$$ $$1$$ $$m/sFor$$ points at a distance of $$2$$ m, $$v2$$ $$=$$ $$2$$ $$m/s$$ and for points at a distance of $$3m$$ , $$v3=3msIf$$ a charge rotating in a circle constitutes a current I,$$B=$$ μ$$0i2r$$,  where i  qt $$=$$ $$qv2$$$$π$$rSince field due to rotation of all charges are in same $$directionB=$$ ∑μ$$0qv4$$$$π$$$$r2=$$μ$$0q4$$π   $$1+1+12$$ $$+12$$ $$+13$$ $$+13$$⇒$$B=$$  $$11$$μ$$0q12$$π

In figure, AB is a non-conducting rod. Equal charges of magnitude q are fixed at various points on the rod as shown. The rod is rotated uniformly about an axis passing through O and perpendicular to its length such that linear speed of the end A or B of the rod is 3 mis. Magnetic field at O is

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