A conducting plate with a uniform surface charge density s = +5.1 x 10 -8 C/m 2

Question

A conducting plate with a uniform surface charge densitys = +5.1 x 10-8C/m2 is spaced a distance d = 2 cm above andparallel to an identical plate with uniform surface charge density-s. The spacing d issmall compared to the x- and z-dimensions of theplates.

(a) What is the y-component of the electric fieldmidway between the plates and far from the edges of the plates?

Ey = V/m    

(b) What is the electric potential of the top plate relative tothe bottom plate?

V1 - V2 = V    

(c) A particle of mass m = 5 g and charge Q =-5 x 10-3 C rests at the bottom side of the top plate.How much work would have to be done on the particle to bring it tothe bottom plate? (Ignore gravity.)

W = J    

(d) If the same particle is subsequently released at rest fromthe bottom plate, with what speed will it impact the top plate?

v = m/s    

(e) Suppose instead the upper plate was moved closer to thelower plate, reducing the spacing to d' = 1.2 cm, withoutchanging the net charges on the upper or lower plates. What wouldthe impact speed be if the same particle were released at rest fromthe lower plate in this case?

v' = m/s

Explanation / Answer

(a) the y-component of the electric field midway between theplates and far from the edges of the plates is                 Ey = / o Here = +5.1 x 10-8C/m2      o =8.85*10-12C2/N.m2 (b) the electric potential of the top plate relative to the bottomplate is           V1 - V2 =Eyd Here Ey is substituted here which is calculated from thepart (a)          d = 2 cm =0.02m (c) The amount of work have to be done on the particle to bring it tothe bottom plate is             W = Fd                 = (Eyq)d = Eyqd Here Ey is substituted here which is calculated from thepart (a)          q =5.0*10-3C          d = 2 cm =0.02m (d) According to the work - energy theorem we have             W = KE                  = (1/2)mv2 - (1/2)mu2                  = (1/2)mv2 - 0      [ since u =0 ]              v = [2W/m] Here W is substituted here which is calculated from the part(c)          m = 5 g =5.0*10-3kg

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