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The largest magnitude the electric field on the axis of a uniformly charged ring of radius 3  m is at a distance h from its centre. What is the value of h ?  Take  1 2 = 0 . 7

Correct answer

2.1

Step-by-step solution

E axial = Q h 4 π ε 0 h 2 + a 2 3 2 where, a = radius of the ring, h = distance of point from the centre. For the maximum value, d E d h = 0 ∴ d dh Qx 4 π ε 0 h 2 + a 2 3 2 = 0 ∴ h 2 + a 2 3 2 - h 3 2 h 2 + a 2 1 2 · ( 2 h ) h 2 + a 2 3 = 0 ∴ h 2 + a 2 - 3 h 2 = 0 ∴ h = ± a 2 = 3 2 m … . ( ∵ a = 3 m ) = 3 × 0 . 7 = 2 . 1 m

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