Three infinite charged plates are placed on an x-axis as shown. Their surface ch

Question

Three infinite charged plates are placed on an x-axis as shown. Their surface charge densities are indicated as multiples of , with = 2 × 10-6 C/m2, we have already determined the electric field created by these plates in each region: the electric field in each region is uniform, and the magnitude and direction are shown 1. Fl = 2.26 × 1051|EI = 4.52 × 105 E=0 E=0 -80 -60 -20 20 60 80 -3 +2 Because they are conductors, the electric potential everywhere on a single charged plate will be the same (i.e., the entire plate is an equipotential). Without doing any calculations, predict which plate will have the highest electric potential and which plate will have the lowest electric potential, or state if any of the plates have the same electric potential. Explain your reasoning. a. b. Calculate the magnitude of the change in electric potential over each of the following intervals: i. From x =-80 m to x =-40 m ii. From x =-40 rn to x = 0 iii. From x = 0 to x = +40pm iv. From x = +40 rn to x = +80 m

Explanation / Answer

from the given data and the diagram
we can see

a. as the electric field has the highest magnitude in the right hand side and is moving away from the right most plate
the right most plate has the highest potential as electric field direction is in the direciton of falling potential
also this plate has the highest positive charge validating our conclusion

no two plates in this case will have same potential

b. i. from x = -80u m to -40 um
E = 0
hence
dV = 0 V

ii. x = -40 um to 0 um
E = 2.26*10^5 N/C
hence dV = -2.26*10^5*40*10^-6 = 9.04 V

iii. x = 0 to x = 40 um
E = -4.52*10^5 N/C
dV = 4.52*10^5*40*10^-6 = 18.08 V

iv. from x = 40 um to x = 80 um
E = 0
hence dV = 0 V

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