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Q.

A ring of radius R has charge Q distributed uniformly on it. At a distance x ( 0) from centre on its axis.(consider axial points only)

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a

Potential cannot be greater than Q4πε0R

b

Electric field cannot be greater than Q63πε0R2

c

For small value of x, a charge - q of mass m released, oscillates with time period of 2π4πε0mR3qQ

d

If x = 0, for a charge - q and mass m, escape velocity is qQ2πε0mR

answer is A, B, C, D.

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Detailed Solution

a) V=KQr r is minimum at x = 0 or  Vmax=KQR

b) E=KQx2R2+x23/2 for Emax,dEdx=0

x=±R2, Emax=Q63πε0R2

 

c) F=qE14πε0Qqx2R3

Using the force law in oscillations, we get ω2=14πε0Qq2R3

d) for just escape total mechanical energy = 0 KQqR+12mv2=0

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