Questions

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 at the end A or B of the rod is 3 ms^{-1}. Magnetic field at O is

a

11μ0q12π

b

3μ0q7π

c

μ0q2π

d

6μ0q13π

detailed solution

Correct option is A

Since the rod is a rigid body, every point has same angular velocity u = 1 rad/s. For points at a distance of 1m, v1 = I m/s For points at a distance of 2 m, v2= 2 m/s If a charge rotating in a circle constitutes a current I.B=μoi2r, where i=qt=qv2πr Since field due to rotation bf all charges are in same direction,, B=∑μoqv4πr2=μoq4π1+1+12+12+13+13

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