One half of a charged thin ring of radius R carries a charge q1 uniformly distributed over it, and the other half of the ring carries a charge q2 uniformly distributed over it. For any position along the axis of symmetry of the ring, derive an expression for (a) the component of the electric field parallel to the axis and (b) the component of the electric field perpendicular to the axis.

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One half of a charged thin ring of radius R carries a charge
q1 uniformly distributed over it, and the other half of the
ring carries a charge q2 uniformly distributed over it. For any
position along the axis of symmetry of the ring, derive an
expression
for (a) the component of the electric field parallel
to the axis and (b) the component of the electric field perpendicular
to the axis.

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