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

Ey =   - 2 x/ 2o = - /o = -5763 V/m    

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

V1 -V2 = E d =115 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 = |V x q| = 0.575J

v = (2V |q| / m)= 15.2 m/s    

v' = (2V' |q| / m)= 11.7 m/s

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