Copper is used to make a sphere [radius = r. mass = M]. It carries a net charge

Question

Copper is used to make a sphere [radius = r. mass = M]. It carries a net charge [-Q_1]. The charged sphere is released from rest at point A, near the surface of the earth. Point A is midway between two oppositely charged square plates [height = H, charge = +/-2Q_1] separated by a distance 'D' The horizontal arrows indicate the direction of the uniform electric field between the plates. The gravitational force on the sphere may not be ignored. if the copper sphere misses the edge of a plate by a distance 6 as it passes through point B, derive an expression for the maximum value of 'H'.

Explanation / Answer

ay = F/m = (Q1*E)/m = (Q1*/0)/m = [Q1*( Q1/4r2)/0]/m = Q12/m 04r2

H= 1/2gt2

t2=(2H/g)

D/2- = 1/2ayt2 = 1/2ay2H = 1/2*[Q12/m 04r2]*(2H/g)

D/2- = [HQ12/mg04r2]

H= (D/2-)/[Q12/mg04r2]

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